Li–Yorke Chaos in Globally Coupled Map Lattice with Delays

Abstract

Delay coupled smooth maps over a ring network with global coupling have been considered. Proof of the existence of chaos in the sense of Li–Yorke in the globally coupled smooth maps with homogeneous unit delay has been given by defining a suitable matrix norm. Conditions for the existence of Li–Yorke chaos depending on the coupling strength, map parameter and lattice size have been derived analytically. Chaotic regions in the parameter space are plotted numerically for delay coupled logistic maps.