Spatio-temporal structures in ensembles of coupled chaotic systems

Abstract

Abstract We review numerical results of studies of the complex dynamics of one- and double-dimensional networks (ensembles) of nonlocally coupled identical chaotic oscillators in the form of discrete- and continuous-time systems, as well as lattices of coupled ensembles. We show that these complex networks can demonstrate specific types of spatio-temporal patterns in the form of chimera states, known as the coexistence of spatially localized domains of coherent (synchronized) and incoherent (asynchronous) dynamics in a network of nonlocally coupled identical oscillators. We describe phase, amplitude, and double-well chimeras and solitary states; their basic characteristics are analyzed and compared. We focus on two basic discrete-time models, Hénon and Lozi maps, which can be used to describe typical chimera structures and solitary states in networks of a wide range of chaotic oscillators. We discuss the bifurcation mechanisms of their appearance and evolution. In conclusion, we describe effects of synchronization of chimera states in coupled ensembles of chaotic maps.