Coupling-induced periodic windows in networked discrete-time systems

TL;DR

This paper investigates how coupling in networked discrete-time systems induces stable periodic behavior from chaotic units, revealing a replication mechanism that enhances stability and synchronization.

Contribution

It uncovers a novel mechanism where network interactions replicate periodic windows, stabilizing chaos and promoting synchronization, with analysis via the master stability function.

Findings

Periodic windows are replicated through coupling.

Network coupling enhances stability against disturbances.

Complete synchronization occurs within these replicated windows.

Abstract

Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit oscillates chaotically if in isolation. Surprisingly, the mechanism in which the network interaction replaces chaos by periodicity is still poorly understood. Here, we show that such an onset of regularity can occur via replication of periodic windows. This phenomenon multiplies the stability domains in the system parameter space, not only suppressing chaos but also making the network less vulnerable to external disturbances such as shocks and noise. Moreover, we observe that the network cluster synchronizes for the parameters corresponding to the replica periodic windows. To confirm these observations, we employ the formalism of the master stability function demonstrating that the complete synchronized state is indeed transversally unstable in the replica windows.