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Cognitive Neurodynamics

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01-04-2013 | Research Article

Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction

Authors: Haixia Wang, Qingyun Wang, Qishao Lu, Yanhong Zheng

Published in: Cognitive Neurodynamics | Issue 2/2013

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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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Boccalettia S, Kurths J, Osipov G, Valladares DL, Zhou CS (2002) The synchronization of chaotic systems. Phys Rep 366:1–101CrossRef

Burić N, Ranković D (2007) Bursting neurons with coupling delays. Phys Lett A 363:282–289CrossRef

Burić N, Todorović K, Vasović N (2008) Synchronization of bursting neurons with delayed chemical synapses. Phys Rev E 78:036211CrossRef

Campbell SA (2007) Introduction to delay differential equations. University of Waterloo, Canada

Dhamala M, Kirsa VK, Ding MZ (2004) Transitions to synchrony in coupled bursting neurons. Phys Rev Lett 92:028101PubMedCrossRef

Dhamala M, Kirsa VK, Ding MZ (2004) Enhancement of neural synchrony by time delay. Phys Rev Lett 92:074104PubMedCrossRef

Fan DJ, Hong L, Wei JJ (2010) Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays. Nonlinear Dyn 62:305–319CrossRef

Fries P (2009) Neuronal gamma-band synchronization as a fundamental process in cortical computation. Annu Rev Neurosci 32:209–224PubMedCrossRef

Gray CM and Singer W (1989) Stimulus-specific neuronal oscillation in orientation columns of cat visual cortex. Proc Natl Acad Sci 86:1698–1702PubMedCrossRef

Hao YH, Gong YB, Wang L, Ma XG, Yang CL (2011) Single or multiple synchronization transitions in scale-free neuronal networks with electrical or chemical coupling. Chaos Solitons Fractals 44:260–268CrossRef

Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc London Ser B 221:87–102CrossRef

Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurcat Chaos Appl Sci Eng 10:1171–1266CrossRef

Izhikevich EM (2005) Dynamical systems in neuroscience: the geometry of excitability and bursting. The MIT Press, Massachusetts

Jalili M (2011) Phase synchronization in Hindmarsh-Rose neural networks with delayed chemical coupling. Neurocomputing 74:1551–1556CrossRef

Kobelevskiy I (2008) Bifurcation analysis of a system of morris-lecar neurons with time delayed gap junctional coupling. University of Waterloo, Canada

Kuznetsov YA (1995) Elements of applied bifurcation theory. Springer, New YorkCrossRef

Levy R, Hutchison WD, Lozano AM, Dostrovsky JO (2000) High-frequency synchronization of neuronal activity in the subthalamic nucleus of Parkinsonian patients with limb tremor. J Neurosci 20:7766–7775PubMed

Lu QS, Peng LP, Yang ZQ (2010) Ordinary differential equation and dynamical system. Beihang University Press, Beijing

Liu Y, Wang R, Zhang Z, Jiao X (2010) Analysis of stability of neural network with inhibitory neurons. Cogn Neurodyn 4:61-68PubMedCrossRef

Ma SQ, Lu QS, Feng ZS (2010) Synchrony and lag synchrony on a neuron model coupling with time delay. Int J Non-linear Mech 45:659–665CrossRef

Nowotny T, Huerta R, Rabinovich MI (2008) Neuronal synchrony: peculiarity and generality. Chaos, Solitons Fractals 18:037119PubMedCrossRef

Ranković D (2011) Bifurcations of FitzhHugh-Nagumo excitable systems with chemical delayed coupling. Matematicki Vesnik 63:103–114

Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Phys Rev Lett 76:1804–1807PubMedCrossRef

Shen Y, Hou ZH, Xin HW (2008) Transition to burst synchronization in coupled neuron networks. Phys Rev E 77:031920CrossRef

Shi X, Lu QS (2007) Rhythm synchronization of coupled neurons with temporal coding scheme. Chin Phys Lett 24:636–639CrossRef

Shi X, Lu QS (2009) Burst synchronization of electrically and chemically coupled map-based neurons. Phys A 388:2410–2419CrossRef

Shi X, Lu QS, Wang HX (2012) In-phase burst synchronization and rhythm dynamics of complex neuronal networks. Int J Bifurcation Chaos 22:1250101CrossRef

Shuai JW, Durand DM (1999) Phase synchronization in two coupled chaotic neurons. Phys Lett A 264:289–297CrossRef

Sterpu M, Rocsoreanu C (2005) Hopf bifurcation in a system of two coupled advertising oscillators. Nonlinear Anal Real World Appl 6:1–12CrossRef

Suykens JAK, Osipov GV (2008) Synchronization in complex networks. Chaos, Solitons Fractals 18:037101PubMedCrossRef

Wang HX, Lu QS, Shi X (2010) Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis. Chin Phys B 19:060509CrossRef

Wang QY, Duan ZS, Feng ZS, Chen GR, Lu QS (2008) Synchronization transition in gap-junction-coupled leech neurons. Phys A 387:4404–4410CrossRef

Wang QY and Lu QS (2005) Time delay-enhanced synchronization and regularization in two coupled chaotic neurons. Chin Phys Lett 22:543–546CrossRef

Wang QY, Perc M, Duan ZS, Chen GR (2009) Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys Rev E 80:026206CrossRef

Wang R, Jiao X (2006) A stochastic nonlinear evolution model and neural coding on neuronal population possessing variable coupling intensity in spontaneous behavior. Neurocomputing 69(7–9):778–785CrossRef

Wang R, Zhang Z (2003) Nonlinear stochastic models of neurons activities. Neurocomputing 51:401–411CrossRef

Zhang X, Wang R, Zhang Z, Qu J, Cao J, Jiao X (2010) Dynamic phase synchronization characteristics of variable high-order coupled neuronal oscillator population. Neurocomputing 73:2665–2670CrossRef

Vaadia E et al. (1995) Dynamics of neuronal interactions in the monkey cortex in relation to behavioral events. Nat Biotechnol 373:515–518PubMedCrossRef

Zheng YH, Lu QS (2008) Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network. Phys A 387:3719–3728CrossRef

Title: Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction
Authors: Haixia Wang
Qingyun Wang
Qishao Lu
Yanhong Zheng
Publication date: 01-04-2013
Publisher: Springer Netherlands
Published in: Cognitive Neurodynamics / Issue 2/2013
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI: https://doi.org/10.1007/s11571-012-9222-0

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