Global topological control for synchronized dynamics on networks

TL;DR

This paper introduces a topology-based control scheme for stabilizing synchronized dynamics in networked multispecies models, demonstrated using the Complex Ginzburg-Landau and real Ginzburg-Landau equations.

Contribution

It presents a novel method to control symmetry breaking in spatially extended networks by modifying topology without changing dynamical parameters.

Findings

Successfully stabilizes synchronous limit cycles in the Complex Ginzburg-Landau model.

Achieves topological stabilization of fixed points in coupled real Ginzburg-Landau equations.

Demonstrates effectiveness for both symmetric and balanced asymmetric network couplings.

Abstract

A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point.