Collective chaos in pulse-coupled neural networks

Abstract

We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the onset of various chimera states as well as to a new regime, where the two populations are characterized by a different degree of synchronization. Symmetric collective states of increasing dynamical complexity are also observed. The computation of the the finite-amplitude Lyapunov exponent allows us to establish the chaoticity of the (collective) dynamics in a finite region of the phase plane. The further numerical study of the standard Lyapunov spectrum reveals the presence of several positive exponents, indicating that the microscopic dynamics is high-dimensional.

6 pages, 5 eps figures, to appear on Europhysics Letters in 2010

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Cited by in corpus (49)

• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Chimera States in Mechanical Oscillator Networks
• Chimera Death: Symmetry Breaking in Dynamical Networks
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Chimera states: The Existence Criteria Revisited
• Coherence-resonance chimeras in a network of excitable elements
• Chimera states in networks of nonlocally coupled Hindmarsh-Rose neuron models
• Low-dimensional dynamics of populations of pulse-coupled oscillators
• Quantum signatures of Chimera states
• Chimera patterns in two-dimensional networks of coupled neurons
• Controlling Chimeras
• Intermittent chaotic chimeras for coupled rotators
• Chimera patterns under the impact of noise
• Basins of Attraction for Chimera States
• From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
• Chimera states in coupled Kuramoto oscillators with inertia
• Amplitude chimeras and chimera death in dynamical networks
• Clustered Chimera States in Systems of Type-I Excitability
• Dynamics of a large system of spiking neurons with synaptic delay
• Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities
• Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons
• On the equivalence of phase-oscillator and integrate-and-fire models
• Three-dimensional chimera patterns in networks of spiking neuron oscillators
• Coherent oscillations in balanced neural networks driven by endogenous fluctuations
• Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems
• Population spiking and bursting in next generation neural masses with spike-frequency adaptation
• Phase-flip chimera induced by environmental nonlocal coupling
• Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling
• Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons
• Marginal chimera state at cross-frequency locking of pulse-coupled neural networks
• From phase to amplitude oscillators
• Emergent excitability in adaptive networks of non-excitable units
• Phase response function for oscillators with strong forcing or coupling
• Chimera-like states in two distinct groups of identical populations of coupled Stuart-Landau oscillators
• Mean field approximation of two coupled populations of excitable units
• Self adaptation of chimera states
• Stable chaos in fluctuation driven neural circuits
• Robust universal approach to identify travelling chimeras and synchronized clusters in spiking networks
• Dynamics of a network of quadratic integrate-and-fire neurons with bimodal heterogeneity
• Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments
• Collective dynamics in the presence of finite-width pulses
• Sisyphus Effect in Pulse Coupled Excitatory Neural Networks with Spike-Timing Dependent Plasticity
• Cellular automaton for chimera states
• Irregular collective dynamics in a Kuramoto-Daido system
• A robust balancing mechanism for spiking neural networks
• Noise-induced chimera states in a neural network
• Multi-chimera states in the Leaky Integrate-and-Fire model
• Chimeras with uniformly distributed heterogeneity: two coupled populations
• Synchronization patterns in LIF Neural Networks: Merging Nonlocal and Diagonal Connectivity