Coherence and Transients in Nonlocally Coupled Dissipative Kicked Rotors

TL;DR

This paper investigates the complex dynamics of nonlocally coupled dissipative kicked rotors, revealing critical transitions, bifurcations, and a novel domain-wall phenomenon with long transient states influenced by coupling parameters.

Contribution

It provides the first detailed analysis of phase transitions and transient phenomena in nonlocally coupled dissipative rotors, highlighting differences from other coupled systems.

Findings

Identification of critical transitions and bifurcations in the phase diagram.

Discovery of a domain-wall phenomenon with long transient states.

Demonstration of how coupling strength and range influence system dynamics.

Abstract

The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling strength and the coupling range, and show both analytically and numerically the critical transitions in the phase diagram, which include bifurcations of simple spatiotemporal patterns and changes in basin sizes of coherent states with different wavenumbers. We highlight that this diagram is fundamentally different from those found in other coupled systems such as in coupled logistic maps or Lorenz systems. Finally, we show an interesting domain-wall phenomenon in the coupled chaotic rotors, where a super-long transient interface state (partially regular and partially chaotic) is observed and can persist exponentially long as the coupling range increases up to a critical threshold.