Abstract

Spatiotemporal behavior of spatially distributed nonequilibrium systems is a crucial problem in complex dynamics. In particular, in high-dimensional chaotic systems, different solutions (spatial structures) coexist in the stationary state. The important fundamental question then arises: What kind of spatiotemporal behavior takes place when coexisting equilibria (patterns) become dynamically unstable? We have investigated this general issue for years, and recently discovered self-induced switching between coexisting attractor ruins by an internally created chaotic force, i.e., chaotic itinerancy, in some high-dimensional chaotic systems including a coupled bistable chain¹, multimode Maxwell-Bloch² and spatially-coupled laser systems.³ The essential common requirements for this phenomenon have been found to be ’coupling’ between elements and ’on-site nonlinearity’. This fact inspired us to investigate a simple model system, the time-dependent Ginzburg-Landau (TDGL) equation system, which includes complex coupling and nonlinearity in a general fashion.⁴ TDGL has been extensively investigated to understand turbulent phenomena in spatially extended nonequilibrium systems. However, attention has been focused on the behavior around the localized equilibrium, and interplay between coexisting equilibria has been left an open question. In this paper, we discuss a discrete TDGL equation with complex coupling coefficients under the periodic boundary condition, which expresses spatiotemporal dynamics of a one- dimensional looped nonlinear oscillator chain, e.g., lasers. We investigate its spatiotemporal dynamics, paying special attention to the interplay between local chaos around coexisting equilibria and the scenario leading to global chaos, which is expected to result from the connection between local chaotic orbits.

© 1991 Optical Society of America