Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li–Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 22-cycles are also shown by simulations for some values of the parameters.

► A globally nonlocal coupled map lattice is introduced. ► A sufficient condition for the existence of Li–Yorke chaos is determined. ► A sufficient condition for synchronous behaviors is obtained.