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Kazemi S, Jamali Y. Phase synchronization and measure of criticality in a network of neural mass models. Sci Rep 2022; 12:1319. [PMID: 35079038 PMCID: PMC8789819 DOI: 10.1038/s41598-022-05285-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2021] [Accepted: 01/10/2022] [Indexed: 11/15/2022] Open
Abstract
Synchronization has an important role in neural networks dynamics that is mostly accompanied by cognitive activities such as memory, learning, and perception. These activities arise from collective neural behaviors and are not totally understood yet. This paper aims to investigate a cortical model from this perspective. Historically, epilepsy has been regarded as a functional brain disorder associated with excessive synchronization of large neural populations. Epilepsy is believed to arise as a result of complex interactions between neural networks characterized by dynamic synchronization. In this paper, we investigated a network of neural populations in a way the dynamics of each node corresponded to the Jansen-Rit neural mass model. First, we study a one-column Jansen-Rit neural mass model for four different input levels. Then, we considered a Watts-Strogatz network of Jansen-Rit oscillators. We observed an epileptic activity in the weak input level. The network is considered to change various parameters. The detailed results including the mean time series, phase spaces, and power spectrum revealed a wide range of different behaviors such as epilepsy, healthy, and a transition between synchrony and asynchrony states. In some points of coupling coefficients, there is an abrupt change in the order parameters. Since the critical state is a dynamic candidate for healthy brains, we considered some measures of criticality and investigated them at these points. According to our study, some markers of criticality can occur at these points, while others may not. This occurrence is a result of the nature of the specific order parameter selected to observe these markers. In fact, The definition of a proper order parameter is key and must be defined properly. Our view is that the critical points exhibit clear characteristics and invariance of scale, instead of some types of markers. As a result, these phase transition points are not critical as they show no evidence of scaling invariance.
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Affiliation(s)
- Sheida Kazemi
- Biomathematics Laboratory, Department of Applied Mathematics, School of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
| | - Yousef Jamali
- Biomathematics Laboratory, Department of Applied Mathematics, School of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran.
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Shena J, Lazarides N, Hizanidis J. Synchronization transitions in a hyperchaotic SQUID trimer. CHAOS (WOODBURY, N.Y.) 2021; 31:093102. [PMID: 34598466 DOI: 10.1063/5.0058249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 08/10/2021] [Indexed: 06/13/2023]
Abstract
The phenomena of intermittent and complete synchronization between two out of three identical, magnetically coupled Superconducting QUantum Interference Devices (SQUIDs) are investigated numerically. SQUIDs are highly nonlinear superconducting oscillators/devices that exhibit strong resonant and tunable response to applied magnetic field(s). Single SQUIDs and SQUID arrays are technologically important solid-state devices, and they also serve as a testbed for exploring numerous complex dynamical phenomena. In SQUID oligomers, the dynamic complexity increases considerably with the number of SQUIDs. The SQUID trimer, considered here in a linear geometrical configuration using a realistic model with experimentally accessible control parameters, exhibits chaotic and hyperchaotic behavior in wide parameter regions. Complete chaos synchronization as well as intermittent chaos synchronization between two SQUIDs of the trimer is identified and characterized using the complete Lyapunov spectrum of the system and appropriate measures. The passage from complete to intermittent synchronization seems to be related to chaos-hyperchaos transitions as has been conjectured in the early days of chaos synchronization.
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Affiliation(s)
- J Shena
- Laboratory for Superconducting Metamaterials, National University of Science and Technology "MISiS," Leninsky Prospect 4, Moscow 119049, Russia
| | - N Lazarides
- Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Greece
| | - J Hizanidis
- Laboratory for Superconducting Metamaterials, National University of Science and Technology "MISiS," Leninsky Prospect 4, Moscow 119049, Russia
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Zirkle J, Rubchinsky LL. Spike-Timing Dependent Plasticity Effect on the Temporal Patterning of Neural Synchronization. Front Comput Neurosci 2020; 14:52. [PMID: 32595464 PMCID: PMC7303326 DOI: 10.3389/fncom.2020.00052] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 05/12/2020] [Indexed: 11/29/2022] Open
Abstract
Neural synchrony in the brain at rest is usually variable and intermittent, thus intervals of predominantly synchronized activity are interrupted by intervals of desynchronized activity. Prior studies suggested that this temporal structure of the weakly synchronous activity might be functionally significant: many short desynchronizations may be functionally different from few long desynchronizations even if the average synchrony level is the same. In this study, we used computational neuroscience methods to investigate the effects of spike-timing dependent plasticity (STDP) on the temporal patterns of synchronization in a simple model. We employed a small network of conductance-based model neurons that were connected via excitatory plastic synapses. The dynamics of this network was subjected to the time-series analysis methods used in prior experimental studies. We found that STDP could alter the synchronized dynamics in the network in several ways, depending on the time scale that plasticity acts on. However, in general, the action of STDP in the simple network considered here is to promote dynamics with short desynchronizations (i.e., dynamics reminiscent of that observed in experimental studies). Complex interplay of the cellular and synaptic dynamics may lead to the activity-dependent adjustment of synaptic strength in such a way as to facilitate experimentally observed short desynchronizations in the intermittently synchronized neural activity.
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Affiliation(s)
- Joel Zirkle
- Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN, United States
| | - Leonid L Rubchinsky
- Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN, United States.,Stark Neurosciences Research Institute, Indiana University School of Medicine, Indianapolis, IN, United States
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Abstract
Difficult tasks are commonly equated with complex tasks across many behaviors. Motor task difficulty is traditionally defined via Fitts' law, using evaluation criteria based on spatial movement constraints. Complexity of data is typically evaluated using non-linear computational approaches. In this project, we investigate the potential to evaluate task difficulty via behavioral (motor performance) complexity in a Fitts-type task. Use of non-linear approaches allows for inclusion of many features of motor actions that are not currently included in the Fitts-type paradigm. Our results indicate that tasks defined as more difficult (using Fitts movement IDs) are not associated with complex motor behaviors; rather, an inverse relationship exists between these two concepts. Use of non-linear techniques allowed for the detection of behavioral differences in motor performance over the entire action trajectory in the presence of action errors and among neutrally co-constrained effectors not detected using traditional Fitts'-type analyses utilizing movement time measures. Our findings indicate that task difficulty may potentially be inferred using non-linear measures, particularly in ecological situations that do not obey the Fitts-type testing paradigm. While we are optimistic regarding these initial findings, further work is needed to assess the full potential of the approach.
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Guevara Erra R, Perez Velazquez JL, Rosenblum M. Neural Synchronization from the Perspective of Non-linear Dynamics. Front Comput Neurosci 2017; 11:98. [PMID: 29123478 PMCID: PMC5662639 DOI: 10.3389/fncom.2017.00098] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Accepted: 10/09/2017] [Indexed: 11/21/2022] Open
Affiliation(s)
- Ramon Guevara Erra
- Laboratoire Psychologie de la Perception, Centre National de la Recherche Scientifique and Université Paris Descartes, Sorbonne Paris Cité, Paris, France
| | - Jose L Perez Velazquez
- Neuroscience and Mental Health Programme and Division of Neurology, Department of Paediatrics, The Ronin Institute, Institute of Medical Science, Hospital for Sick Children, University of Toronto, Toronto, ON, Canada
| | - Michael Rosenblum
- Department of Physics and Astronomy, University of Potsdam, Potsdam, Germany
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Iqbal M, Rehan M, Hong KS. Modeling of inter-neuronal coupling medium and its impact on neuronal synchronization. PLoS One 2017; 12:e0176986. [PMID: 28486505 PMCID: PMC5423630 DOI: 10.1371/journal.pone.0176986] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2017] [Accepted: 04/20/2017] [Indexed: 11/18/2022] Open
Abstract
In this paper, modeling of the coupling medium between two neurons, the effects of the model parameters on the synchronization of those neurons, and compensation of coupling strength deficiency in synchronization are studied. Our study exploits the inter-neuronal coupling medium and investigates its intrinsic properties in order to get insight into neuronal-information transmittance and, there from, brain-information processing. A novel electrical model of the coupling medium that represents a well-known RLC circuit attributable to the coupling medium’s intrinsic resistive, inductive, and capacitive properties is derived. Surprisingly, the integration of such properties reveals the existence of a natural three-term control strategy, referred to in the literature as the proportional integral derivative (PID) controller, which can be responsible for synchronization between two neurons. Consequently, brain-information processing can rely on a large number of PID controllers based on the coupling medium properties responsible for the coherent behavior of neurons in a neural network. Herein, the effects of the coupling model (or natural PID controller) parameters are studied and, further, a supervisory mechanism is proposed that follows a learning and adaptation policy based on the particle swarm optimization algorithm for compensation of the coupling strength deficiency.
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Affiliation(s)
- Muhammad Iqbal
- Department of Computer and Information Sciences, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan
| | - Muhammad Rehan
- Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan
- * E-mail:
| | - Keum-Shik Hong
- Department of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University, Geumjeong-gu, Busan, Republic of Korea
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Ashwin P, Coombes S, Nicks R. Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2016; 6:2. [PMID: 26739133 PMCID: PMC4703605 DOI: 10.1186/s13408-015-0033-6] [Citation(s) in RCA: 103] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Accepted: 10/30/2015] [Indexed: 05/20/2023]
Abstract
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.
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Affiliation(s)
- Peter Ashwin
- Centre for Systems Dynamics and Control, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, Exeter, EX4 4QF, UK.
| | - Stephen Coombes
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Rachel Nicks
- School of Mathematics, University of Birmingham, Watson Building, Birmingham, B15 2TT, UK.
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Ahn S, Rubchinsky LL. Short desynchronization episodes prevail in synchronous dynamics of human brain rhythms. CHAOS (WOODBURY, N.Y.) 2013; 23:013138. [PMID: 23556975 PMCID: PMC3606233 DOI: 10.1063/1.4794793] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these synchronization/desynchronization patterns. We employ recently developed techniques to analyze the fine temporal structure of phase-locking to study the temporal patterning of synchrony of the human brain rhythms. We study neural oscillations recorded by electroencephalograms in α and β frequency bands in healthy human subjects at rest and during the execution of a task. While the phase-locking strength depends on many factors, dynamics of synchrony has a very specific temporal pattern: synchronous states are interrupted by frequent, but short desynchronization episodes. The probability for a desynchronization episode to occur decreased with its duration. The transition matrix between synchronized and desynchronized states has eigenvalues close to 0 and 1 where eigenvalue 1 has multiplicity 1, and therefore if the stationary distribution between these states is perturbed, the system converges back to the stationary distribution very fast. The qualitative similarity of this patterning across different subjects, brain states and electrode locations suggests that this may be a general type of dynamics for the brain. Earlier studies indicate that not all oscillatory networks have this kind of patterning of synchronization/desynchronization dynamics. Thus, the observed prevalence of short (but potentially frequent) desynchronization events (length of one cycle of oscillations) may have important functional implications for the brain. Numerous short desynchronizations (as opposed to infrequent, but long desynchronizations) may allow for a quick and efficient formation and break-up of functionally significant neuronal assemblies.
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Affiliation(s)
- Sungwoo Ahn
- Department of Mathematical Sciences and Center for Mathematical Biosciences, Indiana University Purdue University Indianapolis, Indiana 46032, USA.
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Wang H, Wang Q, Lu Q, Zheng Y. Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction. Cogn Neurodyn 2012; 7:121-31. [PMID: 24427196 DOI: 10.1007/s11571-012-9222-0] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2012] [Revised: 08/30/2012] [Accepted: 09/17/2012] [Indexed: 11/30/2022] Open
Abstract
The properties of equilibria and phase synchronization involving burst synchronization and spike synchronization of two electrically coupled HR neurons are studied in this paper. The findings reveal that in the non-delayed system the existence of equilibria can be turned into intersection of two odd functions, and two types of equilibria with symmetry and non-symmetry can be found. With the stability and bifurcation analysis, the bifurcations of equilibria are investigated. For the delayed system, the equilibria remain unchanged. However, the Hopf bifurcation point is drastically affected by time delay. For the phase synchronization, we focus on the synchronization transition from burst synchronization to spike synchronization in the non-delayed system and the effect of coupling strength and time delay on spike synchronization in delayed system. In addition, corresponding firing rhythms and spike synchronized regions are obtained in the two parameters plane. The results allow us to better understand the properties of equilibria, multi-time-scale properties of synchronization and temporal encoding scheme in neuronal systems.
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Affiliation(s)
- Haixia Wang
- School of Science, Nanjing University of Science and Technology, Nanjing, 210094 China
| | - Qingyun Wang
- Department of Dynamics and Control, Beihang University, Beijing, 100191 China
| | - Qishao Lu
- Department of Dynamics and Control, Beihang University, Beijing, 100191 China
| | - Yanhong Zheng
- Department of Dynamics and Control, Beihang University, Beijing, 100191 China ; School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007 China
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Park C, Rubchinsky LL. Intermittent synchronization in a network of bursting neurons. CHAOS (WOODBURY, N.Y.) 2011; 21:033125. [PMID: 21974660 PMCID: PMC3194790 DOI: 10.1063/1.3633078] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2011] [Accepted: 08/11/2011] [Indexed: 05/31/2023]
Abstract
Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson's disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here, we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently, synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking, and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson's disease.
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Affiliation(s)
- Choongseok Park
- Department of Mathematical Sciences and Center for Mathematical Biosciences, Indiana University Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.
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Ahn S, Park C, Rubchinsky LL. Detecting the temporal structure of intermittent phase locking. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016201. [PMID: 21867267 PMCID: PMC3164807 DOI: 10.1103/physreve.84.016201] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2011] [Revised: 05/03/2011] [Indexed: 05/22/2023]
Abstract
This study explores a method to characterize the temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the time in parts of its phase space away from the synchronization state. Therefore characteristics of dynamics near this state (such as its stability properties and Lyapunov exponents or distributions of the durations of synchronized episodes) do not describe the system's dynamics for most of the time. We consider an approach to characterize the system dynamics in this case by exploring the relationship between the phases on each cycle of oscillations. If some overall level of phase locking is present, one can quantify when and for how long phase locking is lost, and how the system returns back to the phase-locked state. We consider several examples to illustrate this approach: coupled skewed tent maps, the stability of which can be evaluated analytically; coupled Rössler and Lorenz oscillators, undergoing through different intermittency types on the way to phase synchronization; and a more complex example of coupled neurons. We show that the obtained measures can describe the differences in the dynamics and temporal structure of synchronization and desynchronization events for the systems with a similar overall level of phase locking and similar stability of the synchronized state.
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Affiliation(s)
- Sungwoo Ahn
- Department of Mathematical Sciences and Center for Mathematical Biosciences, Indiana University Purdue University Indianapolis, IN 46032, USA
| | - Choongseok Park
- Department of Mathematical Sciences and Center for Mathematical Biosciences, Indiana University Purdue University Indianapolis, IN 46032, USA
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Park C, Worth RM, Rubchinsky LL. Neural dynamics in parkinsonian brain: the boundary between synchronized and nonsynchronized dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:042901. [PMID: 21599224 PMCID: PMC3100589 DOI: 10.1103/physreve.83.042901] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2010] [Indexed: 05/22/2023]
Abstract
Synchronous oscillatory dynamics is frequently observed in the human brain. We analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data from Parkinsonian patients. We show that the experimentally observed intermittent synchrony can be generated just by moderately increased coupling strength in the basal ganglia circuits due to the lack of dopamine. Comparison of the experimental and modeling data suggest that brain activity in Parkinson's disease resides in the large boundary region between synchronized and nonsynchronized dynamics. Being on the edge of synchrony may allow for easy formation of transient neuronal assemblies.
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Affiliation(s)
- Choongseok Park
- Department of Mathematical Sciences and Center for Mathematical Biosciences, Indiana University Purdue University Indianapolis, Indianapolis, Indiana 46202, USA
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Wang Q, Chen G, Perc M. Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling. PLoS One 2011; 6:e15851. [PMID: 21253015 PMCID: PMC3017050 DOI: 10.1371/journal.pone.0015851] [Citation(s) in RCA: 249] [Impact Index Per Article: 19.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2010] [Accepted: 11/25/2010] [Indexed: 11/18/2022] Open
Abstract
This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.
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Affiliation(s)
- Qingyun Wang
- Department of Dynamics and Control, Beihang University, Beijing, China
| | - Guanrong Chen
- Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China
| | - Matjaž Perc
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
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Smeal RM, Ermentrout GB, White JA. Phase-response curves and synchronized neural networks. Philos Trans R Soc Lond B Biol Sci 2010; 365:2407-22. [PMID: 20603361 DOI: 10.1098/rstb.2009.0292] [Citation(s) in RCA: 139] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.
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Affiliation(s)
- Roy M Smeal
- Department of Bioengineering, Brain Institute, University of Utah, Salt Lake City, 20 South 2030 East, UT 84112, USA.
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Wang XJ. Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev 2010; 90:1195-268. [PMID: 20664082 DOI: 10.1152/physrev.00035.2008] [Citation(s) in RCA: 1166] [Impact Index Per Article: 83.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.
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Affiliation(s)
- Xiao-Jing Wang
- Department of Neurobiology and Kavli Institute of Neuroscience, Yale University School of Medicine, New Haven, Connecticut 06520, USA.
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Jalili M. Synchronizing Hindmarsh-Rose neurons over Newman-Watts networks. CHAOS (WOODBURY, N.Y.) 2009; 19:033103. [PMID: 19791983 DOI: 10.1063/1.3157215] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
In this paper, the synchronization behavior of the Hindmarsh-Rose neuron model over Newman-Watts networks is investigated. The uniform synchronizing coupling strength is determined through both numerically solving the network's differential equations and the master-stability-function method. As the average degree is increased, the gap between the global synchronizing coupling strength, i.e., the one obtained through the numerical analysis, and the strength necessary for the local stability of the synchronization manifold, i.e., the one obtained through the master-stability-function approach, increases. We also find that this gap is independent of network size, at least in a class of networks considered in this work. Limiting the analysis to the master-stability-function formalism for large networks, we find that in those networks with size much larger than the average degree, the synchronizing coupling strength has a power-law relation with the shortcut probability of the Newman-Watts network. The synchronization behavior of the network of nonidentical Hindmarsh-Rose neurons is investigated by numerically solving the equations and tracking the average synchronization error. The synchronization of identical Hindmarsh-Rose neurons coupled over clustered Newman-Watts networks, networks with dense intercluster connections but sparsely in intracluster linkage, is also addressed. It is found that the synchronizing coupling strength is influenced mainly by the probability of intercluster connections with a power-law relation. We also investigate the complementary role of chemical coupling in providing complete synchronization through electrical connections.
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Affiliation(s)
- Mahdi Jalili
- Department of Computer Engineering, Sharif University of Technology, Tehran, Iran.
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Wang Q, Perc M, Duan Z, Chen G. Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:026206. [PMID: 19792230 DOI: 10.1103/physreve.80.026206] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2009] [Revised: 06/14/2009] [Indexed: 05/28/2023]
Abstract
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.
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Affiliation(s)
- Qingyun Wang
- State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
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Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators. J Neurosci 2009; 29:5218-33. [PMID: 19386918 DOI: 10.1523/jneurosci.0426-09.2009] [Citation(s) in RCA: 93] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Networks of model neurons were constructed and their activity was predicted using an iterated map based solely on the phase-resetting curves (PRCs). The predictions were quite accurate provided that the resetting to simultaneous inputs was calculated using the sum of the simultaneously active conductances, obviating the need for weak coupling assumptions. Fully synchronous activity was observed only when the slope of the PRC at a phase of zero, corresponding to spike initiation, was positive. A novel stability criterion was developed and tested for all-to-all networks of identical, identically connected neurons. When the PRC generated using N-1 simultaneously active inputs becomes too steep, the fully synchronous mode loses stability in a network of N model neurons. Therefore, the stability of synchrony can be lost by increasing the slope of this PRC either by increasing the network size or the strength of the individual synapses. Existence and stability criteria were also developed and tested for the splay mode in which neurons fire sequentially. Finally, N/M synchronous subclusters of M neurons were predicted using the intersection of parameters that supported both between-cluster splay and within-cluster synchrony. Surprisingly, the splay mode between clusters could enforce synchrony on subclusters that were incapable of synchronizing themselves. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured.
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Optimal spatial synchronization on scale-free networks via noisy chemical synapses. Biophys Chem 2009; 141:175-9. [PMID: 19232814 DOI: 10.1016/j.bpc.2009.01.012] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2008] [Revised: 01/28/2009] [Accepted: 01/28/2009] [Indexed: 11/23/2022]
Abstract
We show that the spatial synchronization of noise-induced excitations on scale-free networks, mediated through nonlinear chemical coupling, depends vitally on the intensity of additive noise and the coupling strength. In particular, a twofold optimization is needed for achieving maximal spatial synchrony, thus indicating the existence of an optimal noise intensity as well as an optimal coupling strength. On the other hand, the traditional linear coupling via gap junctions, while still requiring a fine-tuning of the noise intensity, does not postulate the existence of an optimal coupling strength since the synchronization increases monotonously with the increasing coupling strength. Presented results reveal inherent differences in optimal spatial synchronization evoked by chemical and electrical coupling, and could hence help to pinpoint their specific roles in networked systems.
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Suykens JAK, Osipov GV. Introduction to Focus Issue: synchronization in complex networks. CHAOS (WOODBURY, N.Y.) 2008; 18:037101. [PMID: 19045475 DOI: 10.1063/1.2985139] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Synchronization in large ensembles of coupled interacting units is a fundamental phenomenon relevant for the understanding of working mechanisms in neuronal networks, genetic networks, coupled electrical and laser networks, coupled mechanical systems, networks in social sciences, and others. It relates to mathematical and computational analysis of the existence of different states and its stability, clustering, bifurcations and chaos, robustness and sensitivity analysis, etc., at the intersection between synchronization and pattern formation in complex networks. This interdisciplinary oriented Focus Issue presents recent progress in this area with contributions on generic methods, specific model studies, and applications.
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