Chaotic maps with nonlocal coupling: Lyapunov exponents, synchronization of chaos, and characterization of chimeras

Abstract

Abstract Coupled map lattices are spatially extended systems in which both space and time are discrete but allowing a continuous state variable. They have been intensively studied since they present a rich spatiotemporal dynamics, including intermittency, chimeras, and turbulence. Nonlocally coupled lattices occur in many problems of physical and biological interest, like the interaction among cells mediated by the diffusion of some chemical. In this work we investigate general features of the nonlocal coupling among maps in a regular lattice, focusing on the Lyapunov spectrum of coupled chaotic maps. This knowledge is useful for determining the stability of completely synchronized states. One of the types of nonlocal coupling investigated in this work is a smoothed finite range coupling, for which chimeras are exhibited and characterized using quantitative measures.