Effective dynamics for chaos synchronization in networks with time-varying topology

TL;DR

This paper introduces an effective dynamical framework for analyzing chaos synchronization in networks with time-varying topologies, enabling prediction of long-term behavior from short observations.

Contribution

It presents a novel method to analyze and predict chaos synchronization in networks with changing topologies using weighted averages of all possible configurations.

Findings

Effective quantities can predict long-term dynamics.

Short-term data suffices for long-term predictions.

Constant topology networks can replicate time-varying behavior.

Abstract

A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. These quantities are defined as weighted averages over all possible topologies. We demonstrate that an ensemble of short time observations can be used to predict the long-term behavior of the lattice. Finally, we point out that it is possible to obtain a lattice with constant topology in which the dynamical behavior is asymptotically identical to one of the time-varying topology.