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Yamakou ME, Desroches M, Rodrigues S. Synchronization in STDP-driven memristive neural networks with time-varying topology. J Biol Phys 2023; 49:483-507. [PMID: 37656327 PMCID: PMC10651826 DOI: 10.1007/s10867-023-09642-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2023] [Accepted: 08/07/2023] [Indexed: 09/02/2023] Open
Abstract
Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing P (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing F (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay [Formula: see text], the average degree [Formula: see text], and the rewiring probability [Formula: see text] have some appropriate values. When [Formula: see text], [Formula: see text], and [Formula: see text] are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when F increases, depending on the network topology. It is also found that the time delay [Formula: see text] can induce intermittent CS and PS whose occurrence is independent F. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.
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Affiliation(s)
- Marius E Yamakou
- Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany.
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22, 04103, Leipzig, Germany.
| | - Mathieu Desroches
- MathNeuro Project-Team, Inria Center at Université Côte d'Azur, 2004 route des Lucioles - BP 93, 06902, Cedex, Sophia Antipolis, France
| | - Serafim Rodrigues
- Mathematical, Computational and Experimental Neuroscience, Basque Center for Applied Mathematics, Alameda de Mazzaredo 14, 48009, Bilbao, Spain
- Ikerbasque, Basque Foundation for Science, Plaza Euskadi 5, 48009, Bilbao, Spain
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2
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Yamakou ME, Kuehn C. Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance. Phys Rev E 2023; 107:044302. [PMID: 37198865 DOI: 10.1103/physreve.107.044302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 03/23/2023] [Indexed: 05/19/2023]
Abstract
Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.
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Affiliation(s)
- Marius E Yamakou
- Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22, 04103 Leipzig, Germany
| | - Christian Kuehn
- Faculty of Mathematics, Technical University of Munich, Boltzmannstrasse 3, 85748 Garching bei München, Germany
- Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria
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3
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Parastesh F, Rajagopal K, Jafari S, Perc M, Schöll E. Blinking coupling enhances network synchronization. Phys Rev E 2022; 105:054304. [PMID: 35706266 DOI: 10.1103/physreve.105.054304] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
This paper studies the synchronization of a network with linear diffusive coupling, which blinks between the variables periodically. The synchronization of the blinking network in the case of sufficiently fast blinking is analyzed by showing that the stability of the synchronous solution depends only on the averaged coupling and not on the instantaneous coupling. To illustrate the effect of the blinking period on the network synchronization, the Hindmarsh-Rose model is used as the dynamics of nodes. The synchronization is investigated by considering constant single-variable coupling, averaged coupling, and blinking coupling through a linear stability analysis. It is observed that by decreasing the blinking period, the required coupling strength for synchrony is reduced. It equals that of the averaged coupling model times the number of variables. However, in the averaged coupling, all variables participate in the coupling, while in the blinking model only one variable is coupled at any time. Therefore, the blinking coupling leads to an enhanced synchronization in comparison with the single-variable coupling. Numerical simulations of the average synchronization error of the network confirm the results obtained from the linear stability analysis.
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Affiliation(s)
- Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | | | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, D-10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, D-14473 Potsdam, Germany
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4
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Synchronization in a Multiplex Network of Nonidentical Fractional-Order Neurons. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030169] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in which the orders of the derivatives in the layers are different. It is observed that the intralayer synchronization state occurs in weaker intralayer couplings when using nonidentical fractional-order derivatives rather than integer-order or identical fractional orders. Furthermore, the needed interlayer coupling strength for interlayer near synchronization decreases for lower fractional orders. The dynamics of the neurons in nonidentical layers are also considered. It is shown that in lower fractional orders, the neurons’ dynamics change to periodic when the near synchronization state occurs. Moreover, decreasing the derivative order leads to incrementing the frequency of the bursts in the synchronization manifold, which is in contrast to the behavior of the single neuron.
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5
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Anwar MS, Rakshit S, Ghosh D, Bollt EM. Stability analysis of intralayer synchronization in time-varying multilayer networks with generic coupling functions. Phys Rev E 2022; 105:024303. [PMID: 35291066 DOI: 10.1103/physreve.105.024303] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where each dynamic units in a layer communicate with others through various independent time-varying connection mechanisms. Here, dynamical units within and between layers may be interconnected through arbitrary generic coupling functions. We show that intralayer synchronous state exists as an invariant solution. Using fast-switching stability criteria, we derive the condition for stable coherent state in terms of associated time-averaged network structure, and in some instances we are able to separate the transverse subspace optimally. Using simultaneous block diagonalization of coupling matrices, we derive the synchronization stability condition without considering time-averaged network structure. Finally, we verify our analytically derived results through a series of numerical simulations on synthetic and real-world neuronal networked systems.
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Affiliation(s)
- Md Sayeed Anwar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Erik M Bollt
- Department of Mathematics, Department of Electrical and Computer Engineering, Department of Physics, Clarkson University, Potsdam, New York 13699, USA
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6
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Parastesh F, Mehrabbeik M, Rajagopal K, Jafari S, Perc M. Synchronization in Hindmarsh-Rose neurons subject to higher-order interactions. CHAOS (WOODBURY, N.Y.) 2022; 32:013125. [PMID: 35105127 DOI: 10.1063/5.0079834] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
Higher-order interactions might play a significant role in the collective dynamics of the brain. With this motivation, we here consider a simplicial complex of neurons, in particular, studying the effects of pairwise and three-body interactions on the emergence of synchronization. We assume pairwise interactions to be mediated through electrical synapses, while for second-order interactions, we separately study diffusive coupling and nonlinear chemical coupling. For all the considered cases, we derive the necessary conditions for synchronization by means of linear stability analysis, and we compute the synchronization errors numerically. Our research shows that the second-order interactions, even if of weak strength, can lead to synchronization under significantly lower first-order coupling strengths. Moreover, the overall synchronization cost is reduced due to the introduction of three-body interactions if compared to pairwise interactions.
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Affiliation(s)
- Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran polytechnic), Tehran 159163-4311, Iran
| | - Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran polytechnic), Tehran 159163-4311, Iran
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Tamil Nadu 600069, India
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran polytechnic), Tehran 159163-4311, Iran
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
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7
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Cenk Eser M, Medeiros ES, Riza M, Zakharova A. Edges of inter-layer synchronization in multilayer networks with time-switching links. CHAOS (WOODBURY, N.Y.) 2021; 31:103119. [PMID: 34717318 DOI: 10.1063/5.0065310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/29/2021] [Indexed: 06/13/2023]
Abstract
We investigate the transition to synchronization in a two-layer network of oscillators with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the timescale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical oscillators in the layers, we observe a significant improvement in the system synchronizability; i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching time, the transition from the network state of low inter-layer synchronization to high inter-layer synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as shrinking and ultimately the disappearance of the basin of attraction of a desynchronized network state.
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Affiliation(s)
- Muhittin Cenk Eser
- Department of Physics, Eastern Mediterranean University, 99628 Famagusta, North Cyprus, via Mersin 10, Turkey
| | - Everton S Medeiros
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Mustafa Riza
- Department of Physics, Eastern Mediterranean University, 99628 Famagusta, North Cyprus, via Mersin 10, Turkey
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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8
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Roy M, Poria S, Hens C. Assortativity-induced explosive synchronization in a complex neuronal network. Phys Rev E 2021; 103:062307. [PMID: 34271687 DOI: 10.1103/physreve.103.062307] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.
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Affiliation(s)
- Mousumi Roy
- Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India
| | - Swarup Poria
- Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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9
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Protachevicz PR, Hansen M, Iarosz KC, Caldas IL, Batista AM, Kurths J. Emergence of Neuronal Synchronisation in Coupled Areas. Front Comput Neurosci 2021; 15:663408. [PMID: 33967729 PMCID: PMC8100315 DOI: 10.3389/fncom.2021.663408] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 03/29/2021] [Indexed: 11/13/2022] Open
Abstract
One of the most fundamental questions in the field of neuroscience is the emergence of synchronous behaviour in the brain, such as phase, anti-phase, and shift-phase synchronisation. In this work, we investigate how the connectivity between brain areas can influence the phase angle and the neuronal synchronisation. To do this, we consider brain areas connected by means of excitatory and inhibitory synapses, in which the neuron dynamics is given by the adaptive exponential integrate-and-fire model. Our simulations suggest that excitatory and inhibitory connections from one area to another play a crucial role in the emergence of these types of synchronisation. Thus, in the case of unidirectional interaction, we observe that the phase angles of the neurons in the receiver area depend on the excitatory and inhibitory synapses which arrive from the sender area. Moreover, when the neurons in the sender area are synchronised, the phase angle variability of the receiver area can be reduced for some conductance values between the areas. For bidirectional interactions, we find that phase and anti-phase synchronisation can emerge due to excitatory and inhibitory connections. We also verify, for a strong inhibitory-to-excitatory interaction, the existence of silent neuronal activities, namely a large number of excitatory neurons that remain in silence for a long time.
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Affiliation(s)
- Paulo R Protachevicz
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil
| | - Matheus Hansen
- Computer Science Department, Institute of Science and Technology, Federal University of São Paulo - UNIFESP, São José dos Campos, Brazil
| | - Kelly C Iarosz
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil.,Faculdade de Telêmaco Borba, Telêmaco Borba, Brazil.,Graduate Program in Chemical Engineering, Federal University of Technology Paraná, Ponta Grossa, Brazil
| | - Iberê L Caldas
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil
| | - Antonio M Batista
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil.,Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil
| | - Jürgen Kurths
- Department Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Department of Physics, Humboldt University, Berlin, Germany.,Centre for Analysis of Complex Systems, Sechenov First Moscow State Medical University, Moscow, Russia
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10
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Bahramian A, Parastesh F, Pham VT, Kapitaniak T, Jafari S, Perc M. Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net. CHAOS (WOODBURY, N.Y.) 2021; 31:033138. [PMID: 33810759 DOI: 10.1063/5.0045840] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we propose and study a two-layer network composed of a Petri net in the first layer and a ring of coupled Hindmarsh-Rose neurons in the second layer. Petri nets are appropriate platforms not only for describing sequential processes but also for modeling information circulation in complex systems. Networks of neurons, on the other hand, are commonly used to study synchronization and other forms of collective behavior. Thus, merging both frameworks into a single model promises fascinating new insights into neuronal collective behavior that is subject to changes in network connectivity. In our case, the Petri net in the first layer manages the existence of excitatory and inhibitory links among the neurons in the second layer, thereby making the chemical connections time-varying. We focus on the emergence of different types of collective behavior in the model, such as synchronization, chimeras, and solitary states, by considering different inhibitory and excitatory tokens in the Petri net. We find that the existence of only inhibitory or excitatory tokens disturbs the synchronization of electrically coupled neurons and leads toward chimera and solitary states.
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Affiliation(s)
- Alireza Bahramian
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave., Valiasr Square, Tehran 159163-4311, Iran
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave., Valiasr Square, Tehran 159163-4311, Iran
| | - Viet-Thanh Pham
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Sajad Jafari
- Center for Computational Biology, Chennai Institute of Technology, Chennai, Tamil Nadu 600069, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
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11
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Pal K, Ghosh D, Gangopadhyay G. Synchronization and metabolic energy consumption in stochastic Hodgkin-Huxley neurons: Patch size and drug blockers. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.10.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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12
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Çimen Z, Korkmaz N, Altuncu Y, Kılıç R. Evaluating the effectiveness of several synchronization control methods applying to the electrically and the chemically coupled hindmarsh-rose neurons. Biosystems 2020; 198:104284. [PMID: 33157155 DOI: 10.1016/j.biosystems.2020.104284] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Revised: 10/27/2020] [Accepted: 10/28/2020] [Indexed: 11/15/2022]
Abstract
This study focuses on the synchronization control between the coupled neurons. The achievements of several synchronization control methods have been checked by evaluating the effects of the synaptic coupling weight alteration on the synchronization. Here, a neural ensemble has been constructed by utilizing the Hindmarsh Rose (HR) Neuron Model. The HR neurons have been linked to each other with the bidirectional coupling. The synchrony or the asynchrony states between these coupled neurons have been observed by using the standard deviation results. Here, firstly, the electrically and the chemically coupled HR neurons have been handled without using any control method, separately and the effects of the synaptic coupling weight alteration on the synchronic firing have been assessed by considering the features of the coupling types. Then, while the electrically coupled HR neurons are generally preferred in the available synchronization control studies; the Lyapunov, the back-stepping, and the feedback synchronization control methods have been adapted to both the electrically and the chemically coupled HR neurons. Thus, a remarkable contribution has been provided to the limited number of studies, which are about the synchronization control of the chemically coupled HR neurons. Also, the synchronization control between the electrically or the chemically coupled HR neurons has been provided by the back-stepping method for the first time. Finally, the differences between the membrane potentials of the coupled neurons have been calculated by utilizing an alternative error function. Since this function calculates the amplitude and the phase errors, separately; the effectiveness of these methods can be evaluated correctly in terms of the performing the minimum differences between the neural dynamics.
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Affiliation(s)
- Zühra Çimen
- Department of Electrical & Electronics Engineering, Niğde Ömer Halisdemir University, 51240, Niğde, Turkey.
| | - Nimet Korkmaz
- Department of Clinical Engineering Research Center, Erciyes University, 38039, Kayseri, Turkey.
| | - Yasemin Altuncu
- Department of Electrical & Electronics Engineering, Niğde Ömer Halisdemir University, 51240, Niğde, Turkey.
| | - Recai Kılıç
- Department of Electrical & Electronics Engineering, Erciyes University, 38039, Kayseri, Turkey.
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13
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Chandran P, Gopal R, Chandrasekar VK, Athavan N. Chimera-like states induced by additional dynamic nonlocal wirings. CHAOS (WOODBURY, N.Y.) 2020; 30:063106. [PMID: 32611102 DOI: 10.1063/1.5144929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
We investigate the existence of chimera-like states in a small-world network of chaotically oscillating identical Rössler systems with an addition of randomly switching nonlocal links. By varying the small-world coupling strength, we observe no chimera-like state either in the absence of nonlocal wirings or with static nonlocal wirings. When we give an additional nonlocal wiring to randomly selected nodes and if we allow the random selection of nodes to change with time, we observe the onset of chimera-like states. Upon increasing the number of randomly selected nodes gradually, we find that the incoherent window keeps on shrinking, whereas the chimera-like window widens up. Moreover, the system attains a completely synchronized state comparatively sooner for a lower coupling strength. Also, we show that one can induce chimera-like states by a suitable choice of switching times, coupling strengths, and a number of nonlocal links. We extend the above-mentioned randomized injection of nonlocal wirings for the cases of globally coupled Rössler oscillators and a small-world network of coupled FitzHugh-Nagumo oscillators and obtain similar results.
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Affiliation(s)
- P Chandran
- Department of Physics, H. H. The Rajah's College (affiliated to Bharathidasan University), Pudukkottai 622 001, Tamil Nadu, India
| | - R Gopal
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India
| | - N Athavan
- Department of Physics, H. H. The Rajah's College (affiliated to Bharathidasan University), Pudukkottai 622 001, Tamil Nadu, India
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14
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Rakshit S, Bera BK, Ghosh D. Invariance and stability conditions of interlayer synchronization manifold. Phys Rev E 2020; 101:012308. [PMID: 32069525 DOI: 10.1103/physreve.101.012308] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Indexed: 11/07/2022]
Abstract
We investigate interlayer synchronization in a stochastic multiplex hypernetwork which is defined by the two types of connections, one is the intralayer connection in each layer with hypernetwork structure and the other is the interlayer connection between the layers. Here all types of interactions within and between the layers are allowed to vary with a certain rewiring probability. We address the question about the invariance and stability of the interlayer synchronization state in this stochastic multiplex hypernetwork. For the invariance of interlayer synchronization manifold, the adjacency matrices corresponding to each tier in each layer should be equal and the interlayer connection should be either bidirectional or the interlayer coupling function should vanish after achieving the interlayer synchronization state. We analytically derive a necessary-sufficient condition for local stability of the interlayer synchronization state using master stability function approach and a sufficient condition for global stability by constructing a suitable Lyapunov function. Moreover, we analytically derive that intralayer synchronization is unattainable for this network architecture due to stochastic interlayer connections. Remarkably, our derived invariance and stability conditions (both local and global) are valid for any rewiring probabilities, whereas most of the previous stability conditions are only based on a fast switching approximation.
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Affiliation(s)
- Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Bidesh K Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India.,Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion, 8499000, Israel
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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15
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Rakshit S, Bera BK, Kurths J, Ghosh D. Enhancing synchrony in multiplex network due to rewiring frequency. Proc Math Phys Eng Sci 2019. [DOI: 10.1098/rspa.2019.0460] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Most of the previous studies on synchrony in multiplex networks have been investigated using different types of intralayer network architectures which are either static or temporal. Effect of a temporal layer on intralayer synchrony in a multilayered network still remains elusive. In this paper, we discuss intralayer synchrony in a multiplex network consisting of static and temporal layers and how a temporal layer influences other static layers to enhance synchrony simultaneously. We analytically derive local stability conditions for intralayer synchrony based on the master stability function approach. The analytically derived results are illustrated by numerical simulations on up to five-layers multiplex networks with the paradigmatic Lorenz system as the node dynamics in each individual layer.
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Affiliation(s)
- Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Bidesh K. Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Zhou S, Guo Y, Liu M, Lai YC, Lin W. Random temporal connections promote network synchronization. Phys Rev E 2019; 100:032302. [PMID: 31639942 DOI: 10.1103/physreve.100.032302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2018] [Indexed: 06/10/2023]
Abstract
We report a phenomenon of collective dynamics on discrete-time complex networks: a random temporal interaction matrix even of zero or/and small average is able to significantly enhance synchronization with probability one. According to current knowledge, there is no verifiably sufficient criterion for the phenomenon. We use the standard method of synchronization analytics and the theory of stochastic processes to establish a criterion, by which we rigorously and accurately depict how synchronization occurring with probability one is affected by the statistical characteristics of the random temporal connections such as the strength and topology of the connections as well as their probability distributions. We also illustrate the enhancement phenomenon using physical and biological complex dynamical networks.
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Affiliation(s)
- Shijie Zhou
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
- School of Mathematical Science, Fudan University, Shanghai 200433, China
- Shanghai Center of Mathematical Sciences, Shanghai 200433, China
| | - Yao Guo
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
| | - Maoxing Liu
- Department of Mathematics, North University of China, Taiyuan 030051, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA
| | - Wei Lin
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
- School of Mathematical Science, Fudan University, Shanghai 200433, China
- Shanghai Center of Mathematical Sciences, Shanghai 200433, China
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
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17
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Majhi S, Bera BK, Ghosh D, Perc M. Chimeras at the interface of physics and life sciences: Reply to comments on "Chimera states in neuronal networks: A review". Phys Life Rev 2019; 28:142-147. [PMID: 31147278 DOI: 10.1016/j.plrev.2019.04.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Accepted: 04/02/2019] [Indexed: 11/25/2022]
Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Bidesh K Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India; Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia; Complexity Science Hub Vienna, Josefstädterstraße 39, A-1080 Vienna, Austria.
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18
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Bera BK, Rakshit S, Ghosh D, Kurths J. Spike chimera states and firing regularities in neuronal hypernetworks. CHAOS (WOODBURY, N.Y.) 2019; 29:053115. [PMID: 31154769 DOI: 10.1063/1.5088833] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2019] [Accepted: 04/24/2019] [Indexed: 06/09/2023]
Abstract
A complex spatiotemporal pattern with coexisting coherent and incoherent domains in a network of identically coupled oscillators is known as a chimera state. Here, we report the emergence and existence of a novel type of nonstationary chimera pattern in a network of identically coupled Hindmarsh-Rose neuronal oscillators in the presence of synaptic couplings. The development of brain function is mainly dependent on the interneuronal communications via bidirectional electrical gap junctions and unidirectional chemical synapses. In our study, we first consider a network of nonlocally coupled neurons where the interactions occur through chemical synapses. We uncover a new type of spatiotemporal pattern, which we call "spike chimera" induced by the desynchronized spikes of the coupled neurons with the coherent quiescent state. Thereafter, imperfect traveling chimera states emerge in a neuronal hypernetwork (which is characterized by the simultaneous presence of electrical and chemical synapses). Using suitable characterizations, such as local order parameter, strength of incoherence, and velocity profile, the existence of several dynamical states together with chimera states is identified in a wide range of parameter space. We also investigate the robustness of these nonstationary chimera states together with incoherent, coherent, and resting states with respect to initial conditions by using the basin stability measurement. Finally, we extend our study for the effect of firing regularity in the observed states. Interestingly, we find that the coherent motion of the neuronal network promotes the entire system to regular firing.
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Affiliation(s)
- Bidesh K Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
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Different properties of neuronal networks matter for the emergence of chimera states: Comment on "Chimera states in neuronal networks: A review" by Majhi et al. Phys Life Rev 2019; 28:128-130. [PMID: 30827847 DOI: 10.1016/j.plrev.2019.02.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Accepted: 02/20/2019] [Indexed: 01/08/2023]
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Chowdhury SN, Ghosh D. Synchronization in dynamic network using threshold control approach. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/125/10011] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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