Network topology and collapse of collective stable chaos

TL;DR

This paper investigates how network topology influences the emergence and collapse of collective stable chaos in coupled map systems, revealing that long-range interactions can suppress chaos and promote synchronization.

Contribution

It demonstrates that the topology of small-world networks can induce the collapse of collective stable chaos, a phenomenon not previously characterized.

Findings

Collective chaos is inhibited at certain rewiring probabilities.

Long-range interactions can induce collapse of stable chaos.

Systems reach synchronized states matching local dynamics.

Abstract

Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotemporal systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of connectivity on the emergence and collapse of collective stable chaos in systems of coupled maps defined on a small-world networks. As local dynamics we employ a map that exhibits a period-three superstable orbit. The network is characterized by a rewiring probability $p$. We find that collective chaos is inhibited on some ranges of values of the probability $p$; instead, in these regions the system reaches a synchronized state equal to the period-three orbit of the local dynamics. Our results show that the presence of long-range interactions can induce the collapse of collective stable chaos in spatiotemporal systems.