Collective dynamics in sparse networks

Abstract

The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a finite connectivity (of the order of a few tens) is able to sustain a nontrivial collective dynamics even in the thermodynamic limit. Although the network structure implies a non-additive dynamics, the microscopic evolution is extensive (i.e. the number of active degrees of freedom is proportional to the number of network elements).

5 pages, 4 figures, to appear in Physical Review Letters

References in corpus (9)

• Synchronization in complex networks
• Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators
• Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
• Breaking Synchrony by Heterogeneity in Complex Networks
• Collective behavior of heterogeneous neural networks
• Noiseless Collective Motion out of Noisy Chaos
• Lyapunov analysis captures the collective dynamics of large chaotic systems
• Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems
• The Peculiar Phase Structure of Random Graph Bisection

Cited by in corpus (17)

• A Brief History of Excitable Map-Based Neurons and Neural Networks
• Transition from asynchronous to oscillatory dynamics in balanced spiking networks with instantaneous synapses
• From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
• Dynamics of a large system of spiking neurons with synaptic delay
• Coherence resonance in neuronal populations: mean-field versus network model
• Death and rebirth of neural activity in sparse inhibitory networks
• Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination
• Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity
• Stable chaos in fluctuation driven neural circuits
• A microscopic mechanism for self-organized quasi periodicity in random networks of non linear oscillators
• Neural Activity of Heterogeneous Inhibitory Spiking Networks with Delay
• Stochastic mean field formulation of the dynamics of diluted neural networks
• Synchronization in populations of sparsely connected pulse-coupled oscillators
• Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks
• Partially unstable attractors in networks of forced integrate-and-fire oscillators
• Collective excitability in highly diluted networks of rotators
• Dynamics and computation in mixed networks containing neurons that accelerate towards spiking