Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons

Abstract

We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or `short-cuts' and the delay in the neuronal interactions. Persistent activity arises for a small fraction of `short-cuts', while a transition to failure occurs at a critical value of the `short-cut' density. The persistent activity consists of multi-stable periodic attractors, the number of which is at least on the order of the number of neurons in the network. For long enough delays, network activity at high `short-cut' densities is shown to exhibit exceedingly long chaotic transients whose failure-times averaged over many network configurations follow a stretched exponential. We show how this functional form arises in the ensemble-averaged activity if each network realization has a characteristic failure-time which is exponentially distributed.

arXiv comment14 pages 23 figures

References in corpus (12)

• Statistical mechanics of complex networks
• Synchronization in small-world systems
• Scaling and percolation in the small-world network model
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Fast Response and Temporal Coding on Coherent Oscillations in Small-World Networks
• Small world effect in an epidemiological model
• Synchronization on small-world networks
• Mean-field solution of the small-world network model
• Self-sustained activity in a small-world network of excitable neurons
• Long Chaotic Transients in Complex Networks
• Physical realizability of small-world networks
• Periodic Neural Activity Induced by Network Complexity

Cited by in corpus (12)

• Evolving networks in the human epileptic brain
• On the Dynamical Complexity of Small-World Networks of Spiking Neurons
• Optimization in Networks
• Self-Sustaining Oscillations in Complex Networks of Excitable Elements
• Multistability, local pattern formation, and global collective firing in a small-world network of non-leaky integrate-and-fire neurons
• Impact of Inter-Country Distances on International Tourism
• Complex self-sustained oscillation patterns in modular excitable networks
• FNS: an event-driven spiking neural network simulator based on the LIFL neuron model
• Effect of Inter-Modular Connection on Fast Sparse Synchronization in Clustered Small-World Neural Networks
• Effect of Small-World Connectivity on Fast Sparsely Synchronized Cortical Rhythms
• Noise-Induced Burst and Spike Synchronizations in An Inhibitory Small-World Network of Subthreshold Bursting Neurons
• Untersuchungen zur Modellierung und Schaltungsrealisierung von synaptischer Plastizitaet