Multi-chimera states in the Leaky Integrate-and-Fire model

We study the dynamics of identical leaky integrate-and-fire neurons with symmetric non-local coupling. Upon varying control parameters (coupling strength, coupling range, refractory period) we investigate the system's behaviour and highlight the formation of chimera states. We show that the introduction of a refractory period enlarges the parameter region where chimera states appear and affects the chimera multiplicity.

[1]  Philipp Hövel,et al.  Robustness of chimera states for coupled FitzHugh-Nagumo oscillators. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[3]  L. Schimansky-Geier,et al.  Ensembles of excitable two-state units with delayed feedback. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Laurent Larger,et al.  Virtual chimera states for delayed-feedback systems. , 2013, Physical review letters.

[5]  Antonio Politi,et al.  Irregular collective behavior of heterogeneous neural networks. , 2010, Physical review letters.

[6]  S. Strogatz,et al.  Solvable model for chimera states of coupled oscillators. , 2008, Physical review letters.

[7]  István Z. Kiss,et al.  Spatially Organized Dynamical States in Chemical Oscillator Networks: Synchronization, Dynamical Differentiation, and Chimera Patterns , 2013, PloS one.

[8]  D. Abrams,et al.  Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators , 2014, 1403.6204.

[9]  K. Showalter,et al.  Chimera and phase-cluster states in populations of coupled chemical oscillators , 2012, Nature Physics.

[10]  Simona Olmi,et al.  Coherent periodic activity in excitatory Erdös-Renyi neural networks: the role of network connectivity. , 2011, Chaos.

[11]  M. Zare,et al.  Cooperation in neural systems: bridging complexity and periodicity. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Simona Olmi,et al.  Collective chaos in pulse-coupled neural networks , 2010, 1010.2957.

[13]  B. Ermentrout.  Neural networks as spatio-temporal pattern-forming systems , 1998 .

[14]  Nicolas Brunel,et al.  Lapicque’s 1907 paper: from frogs to integrate-and-fire , 2007, Biological Cybernetics.

[15]  O. Hallatschek,et al.  Chimera states in mechanical oscillator networks , 2013, Proceedings of the National Academy of Sciences.

[16]  Philipp Hövel,et al.  When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. , 2012, Physical review letters.

[17]  Iryna Omelchenko,et al.  Clustered chimera states in systems of type-I excitability , 2014 .

[18]  Lutz Schimansky-Geier,et al.  Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  R. Roy,et al.  Experimental observation of chimeras in coupled-map lattices , 2012, Nature Physics.

[20]  Y. Kuramoto,et al.  Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators , 2002, cond-mat/0210694.

[21]  S. Strogatz,et al.  Chimera states for coupled oscillators. , 2004, Physical review letters.

[22]  Anastasios Bezerianos,et al.  Chimera States in Networks of Nonlocally Coupled Hindmarsh-Rose Neuron Models , 2013, Int. J. Bifurc. Chaos.

[23]  Steven H. Strogatz,et al.  Chimera States in a Ring of Nonlocally Coupled oscillators , 2006, Int. J. Bifurc. Chaos.

[24]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .