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Qian Y, Han J, Yang R, Chen W, Lei Z, Zheng Z. Emergence of chimeralike oscillation modes in excitable complex networks with preferentially cutting-rewiring operation. CHAOS (WOODBURY, N.Y.) 2024; 34:063143. [PMID: 38934725 DOI: 10.1063/5.0167251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 06/05/2024] [Indexed: 06/28/2024]
Abstract
In this paper, the preferentially cutting-rewiring operation (PCRO) consisting of the cutting procedure and the rewiring procedure is proposed and is applied on an excitable Erdös-Rényi random network (EERRN), by which the structure of the initially homogeneous network changes dramatically, and lots of common leaves (CLs) are formed between the two hubs. Subsequently, besides the single-mode oscillations that can be usually observed in homogeneous excitable systems, a new kind of multi-mode oscillations composed of synchronous and asynchronous parts can self-organize to emerge, which are similar to the coherent and incoherent clusters in traditional chimera states and are consequently named as the chimeralike oscillation modes (CLOMs). Importantly, by utilizing the dominant phase-advanced driving method, both the mechanisms for the formation and the emergence of CLOMs in EERRNs with PCRO are well explained, among which the CL is exposed to play a key role in forming the CLOMs. Furthermore, the PCRO-induced CLOM phenomena can also be observed in other paradigmatic network models or with other paradigmatic excitable dynamics, which definitely confirms that the PCRO is an universal method in inducing the CLOMs in excitable complex networks. Our contributions may shed lights on a new perspective of the emergence of CLOMs in complex systems and would have great impacts in related fields.
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Affiliation(s)
- Yu Qian
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Jing Han
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Runru Yang
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Wentao Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China
| | - Zhao Lei
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Zhigang Zheng
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China
- College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
- School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
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Muolo R, Njougouo T, Gambuzza LV, Carletti T, Frasca M. Phase chimera states on nonlocal hyperrings. Phys Rev E 2024; 109:L022201. [PMID: 38491593 DOI: 10.1103/physreve.109.l022201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 01/08/2024] [Indexed: 03/18/2024]
Abstract
Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data, that complex systems are composed of multiple units experiencing many-body interactions that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a topology solely involving many-body, nonlocal, and nonregular interactions, hereby named nonlocal d-hyperring, (d+1) being the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and we show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are "flattened" to pairwise ones, the chimera behavior is weaker and more elusive.
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Affiliation(s)
- Riccardo Muolo
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Thierry Njougouo
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
- Faculty of Computer Science, University of Namur, B5000 Namur, Belgium
- Department of Electrical and Electronic Engineering, University of Buea, P.O. Box 63, Buea, Cameroon
| | - Lucia Valentina Gambuzza
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
| | - Timoteo Carletti
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Mattia Frasca
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
- Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", IASI-CNR, 00185 Roma, Italy
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Chen D, Li J, Yuan C, He J, Zhu W. Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning. Front Neurosci 2023; 17:1246778. [PMID: 37829719 PMCID: PMC10564988 DOI: 10.3389/fnins.2023.1246778] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2023] [Accepted: 09/07/2023] [Indexed: 10/14/2023] Open
Abstract
Introduction In recent years, extensive research has been conducted on the synchronous behavior of neural networks. It is found that the synchronization ability of neurons is related to the performance of signal reception and transmission between neurons, which in turn affects the function of the organism. However, most of the existing synchronization methods are faced with two difficulties, one is the structural parameter dependency, which limits the promotion and application of synchronous methods in practical problems. The other is the limited adaptability, that is, even when faced with the same control tasks, for most of the existing control methods, the control parameters still need to be retrained. To this end, the present study investigates the synchronization problem of the fractional-order HindmarshRose (FOHR) neuronal models in unknown dynamic environment. Methods Inspired by the human experience of knowledge acquiring, memorizing, and application, a learning-based sliding mode control algorithm is proposed by using the deterministic learning (DL) mechanism. Firstly, the unknown dynamics of the FOHR system under unknown dynamic environment is locally accurately identified and stored in the form of constant weight neural networks through deterministic learning without dependency of the system parameters. Then, based on the identified and stored system dynamics, the model-based and relearning-based sliding mode controller are designed for similar as well as new synchronization tasks, respectively. Results The synchronization process can be started quickly by recalling the empirical dynamics of neurons. Therefore, fast synchronization effect is achieved by reducing the online computing time. In addition, because of the convergence of the identification and synchronization process, the control experience can be constantly replenished and stored for reutilization, so as to improve the synchronization speed and accuracy continuously. Discussion The thought of this article will also bring inspiration to the related research in other fields.
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Affiliation(s)
- Danfeng Chen
- School of Mechatronic Engineering and Automation, Foshan University, Foshan, China
| | - Junsheng Li
- School of Mechatronic Engineering and Automation, Foshan University, Foshan, China
| | - Chengzhi Yuan
- Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, United States
| | - Jun He
- School of Mechatronic Engineering and Automation, Foshan University, Foshan, China
| | - Wenbo Zhu
- School of Mechatronic Engineering and Automation, Foshan University, Foshan, China
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Kongni SJ, Nguefoue V, Njougouo T, Louodop P, Ferreira FF, Tchitnga R, Cerdeira HA. Phase transitions on a multiplex of swarmalators. Phys Rev E 2023; 108:034303. [PMID: 37849080 DOI: 10.1103/physreve.108.034303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 08/01/2023] [Indexed: 10/19/2023]
Abstract
Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range r_{c} which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync π has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength σ_{r} is very small for a fixed r_{c} and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of r_{c}. For σ_{r}=0 and for sufficiently small values of r_{c}, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling σ_{a} and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as σ_{a} increases. These results are supported by simulations and animations added as supplemental materials.
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Affiliation(s)
- Steve J Kongni
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon
| | - Venceslas Nguefoue
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon
| | - Thierry Njougouo
- Faculty of Computer Science and naXys Institute, University of Namur, 5000 Namur, Belgium; Namur Institute for Complex Systems (naXys), University of Namur, Belgium; Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P. O. Box 63, Buea, Cameroon; and MoCLiS Research Group, Dschang, Cameroon
| | - Patrick Louodop
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon; ICTP South American Institute for Fundamental Research, São Paulo State University (UNESP), Instituto de Física Teórica, 01140-070 São Paulo, Brazil; and MoCLiS Research Group, Dschang, Cameroon
| | - Fernando Fagundes Ferreira
- Center for Interdisciplinary Research on Complex Systems, University of Sao Paulo, São Paulo 03828-000, Brazil; and Department of Physics-FFCLRP, University of São Paulo, Ribeirão Preto, SP 14040-901, Brazil
| | - Robert Tchitnga
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon
| | - Hilda A Cerdeira
- São Paulo State University (UNESP), Instituto de Física Teórica, 01140-070 São Paulo, Brazil and Epistemic, Gomez & Gomez Ltda. ME, 05305-031 São Paulo, Brazil
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Explosive transitions to synchronization in networks of frequency dipoles. PLoS One 2022; 17:e0274807. [PMID: 36126075 PMCID: PMC9488809 DOI: 10.1371/journal.pone.0274807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 09/03/2022] [Indexed: 12/02/2022] Open
Abstract
We reveal that an introduction of frequency-weighted inter-layer coupling term in networks of frequency dipoles can induce explosive synchronization transitions. The reason for explosive synchronization is that the oscillators with synchronization superiority are moderately suppressed. The findings show that a super-linear correlation induces explosive synchronization in networks of frequency dipoles, while a linear or sub-linear correlation excites chimera-like states. Clearly, the synchronization transition mode of networks of frequency dipoles is controlled by the power-law exponent. In addition, by means of the mean-field approximation, we obtain the critical values of the coupling strength within and between layers in two limit cases. The results of theoretical analysis are in good agreement with those of numerical simulation. Compared with the previous models, the model proposed in this paper retains the topological structure of network and the intrinsic properties of oscillators, so it is easy to realize pinning control.
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Mehrabbeik M, Parastesh F, Ramadoss J, Rajagopal K, Namazi H, Jafari S. Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:9394-9409. [PMID: 34814351 DOI: 10.3934/mbe.2021462] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.
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Affiliation(s)
- Mahtab Mehrabbeik
- 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
| | - Janarthanan Ramadoss
- Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
| | - Hamidreza Namazi
- School of Engineering, Monash University, Selangor, Malaysia
- College of Engineering and Science, Victoria University, Melbourne, Australia
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
- Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
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Bera BK, Kundu S, Muruganandam P, Ghosh D, Lakshmanan M. Spiral wave chimera-like transient dynamics in three-dimensional grid of diffusive ecological systems. CHAOS (WOODBURY, N.Y.) 2021; 31:083125. [PMID: 34470253 DOI: 10.1063/5.0062566] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional medium through local diffusion. We explore the transition scenarios among several collective dynamical behaviors together with transient spiral wave chimera-like states and investigate the long time behavior of these states. The transition from the transient spiral chimera-like pattern to the long time synchronized or desynchronized pattern appears through the deformation of the incoherent region of the spiral core. We discuss the transient dynamics under the influence of the species diffusion at different time instants. By calculating the instantaneous strength of incoherence of the populations, we estimate the duration of the transient dynamics characterized by the persistence of the chimera-like spatial coexistence of coherent and incoherent patterns over the spatial domain. We generalize our observations on the transient dynamics in a three-dimensional grid of diffusive ecological systems by considering two different prey-predator systems.
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Affiliation(s)
- Bidesh K Bera
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
| | - Srilena Kundu
- 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
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620024, India
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