Desynchronization in diluted neural networks

Abstract

The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase-locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of ``stable chaos'', i.e. by observing that the stochastic-like behaviour is "limited" to a an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.

11 pages, 13 figures, submitted to Phys. Rev. E

References in corpus (7)

• From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
• Desynchronized stable states in diluted neural networks
• Desynchronization in diluted neural networks
• Long Chaotic Transients in Complex Networks
• A new approach to partial synchronization in globally coupled rotators
• Dynamical Motifs: Building Blocks of Complex Network Dynamics
• On the relationship between directed percolation and the synchronization transition in spatially extended systems

Cited by in corpus (36)

• Self-sustained asynchronous irregular states and Up/Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons
• Decorrelation of neural-network activity by inhibitory feedback
• Stable Irregular Dynamics in Complex Neural Networks
• Desynchronization in diluted neural networks
• Desynchronized stable states in diluted neural networks
• Collective behavior of heterogeneous neural networks
• Stability of the splay state in pulse--coupled networks
• Collective oscillations in disordered neural networks
• The simplest problem in the collective dynamics of neural networks: Is synchrony stable?
• Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics
• Self-sustained irregular activity in an ensemble of neural oscillators
• Death and rebirth of neural activity in sparse inhibitory networks
• Recurrent events of synchrony in complex networks of pulse-coupled oscillators
• Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons
• Ubiquity of collective irregular dynamics in balanced networks of spiking neurons
• Stability of splay states in globally coupled rotators
• Cell assembly dynamics of sparsely-connected inhibitory networks: a simple model for the collective activity of striatal projection neurons
• Chaos and correlated avalanches in excitatory neural networks with synaptic plasticity
• Stability of the splay state in networks of pulse-coupled neurons
• Splay states in finite pulse-coupled networks of excitable neurons
• Linear stability in networks of pulse-coupled neurons
• Phenomenology of coupled non linear oscillators
• Influence of synaptic interaction on firing synchronization and spike death in excitatory neuronal networks
• Effective low-dimensional dynamics of a mean-field coupled network of slow-fast spiking lasers
• Stable chaos in fluctuation driven neural circuits
• Dynamical formation of stable irregular transients in discontinuous map systems
• Neural Activity of Heterogeneous Inhibitory Spiking Networks with Delay
• Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles
• Complexity and transition to chaos in coupled Adler-type oscillators
• Stochastic mean field formulation of the dynamics of diluted neural networks
• Synchronization in populations of sparsely connected pulse-coupled oscillators
• Statistical mechanics of phase-space partitioning in large-scale spiking neuron circuits
• Partially unstable attractors in networks of forced integrate-and-fire oscillators
• Dynamics and computation in mixed networks containing neurons that accelerate towards spiking
• Non-linear oscillators with Kuramoto-like local coupling: Complexity analysis and spatiotemporal pattern generation
• Extreme value theory of evolving phenomena in complex dynamical systems: firing cascades in a model of neural network