Effect of Levy noise on the network of coupled Chialvo neurons: Impact of topology

TL;DR

This study explores how Levy noise influences the complex dynamics of coupled Chialvo neuron networks across different topologies, revealing new patterns and control mechanisms for synchronization and wave formation.

Contribution

It introduces the impact of Levy noise on various network topologies of Chialvo neurons, demonstrating novel dynamical behaviors and pattern formations not previously documented.

Findings

Levy noise induces new collective dynamics like standing and traveling waves.

Electromagnetic flux and noise lead to diverse behaviors including spiral wave chimeras.

Delay and coupling affect the stability of patterns such as spirals and target waves.

Abstract

This research investigates the complex spatiotemporal behaviors of Chialvo neuron maps under the influence of Levy noise on three different network topologies that is a ring network, a two dimensional lattice affected by electromagnetic flux, and a delayed coupled lattice. On the ring structure, we show that adding non uniform Levy noise induces the formation of new collective dynamics like standing and traveling waves. The frequency and type of these emergent patterns depend sensitively on the intrinsic excitability parameter and the noise intensity, revealing new pathways to control synchronization behavior through noise modulation. In the 2D lattice network, we show that electromagnetic flux and noise together induce a diverse range of behaviors, from synchronized waves to desynchronized states. Most strikingly, spiral wave chimeras emerge under moderate noise, with coherent and incoherent regions coexisting, highlighting the fine balance between external forcing and stochastic perturbations. Finally, upon introducing delay in the lattice structure, the system displays a rich variety of dynamical regimes such as labyrinth patterns, rotating spirals, and target waves whose stability and transitions are greatly affected by both delay and coupling strength.