Rich Dynamics Caused by a Fractional Diffusion Operator in Nonchaotic Rulkov Maps

There are few works about Neimark–Sacker bifurcating analysis on discrete dynamical systems with linear diffusion and delayed coupling under periodic/Neumann-boundary conditions. In this paper, we build up the framework for Neimark–Sacker bifurcations caused by Turing instability on high-dimensional discrete-time dynamical systems with symmetrical property in the linearized system. The fractional diffusion operator in higher-dimensional discrete dynamical systems is introduced and regular/chaotic Turing patterns are discovered by the computation of the largest Lyapunov exponents.