Coupling-induced periodic windows in networked discrete-time systems

¹ Institut für Theoretische Physik, Technische Universität Berlin - Hardenbergstraße 36, 10623 Berlin, Germany
² Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg 26111 Oldenburg, Germany
³ Departamento de Física, Universidade Federal de São Paulo, UNIFESP - 09913-030, Campus Diadema, São Paulo, Brazil
⁴ Departamento de Física, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, UNESP 13506-900, Campus Rio Claro, São Paulo, Brazil

^(a) eucaotico@gmail.com (corresponding author)

Received: 30 November 2021
Accepted: 25 March 2022

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.