Intermittency and Synchronisation in Gumowski-Mira Maps

Abstract

The Gumowski-Mira map is a 2-dimensional recurrence relation that provide a large variety of phase space plots resembling fractal patterns of nature. We investigate the nature of the dynamical states that produce these patterns and find that they correspond to Type I intermittency near periodic cycles. By coupling two GM maps, such patterns can be wiped out to give synchronised periodic states of lower order.The efficiency of the coupling scheme is established by analysing the error function dynamics.