The dynamics of a symmetric coupling of three modified quadratic maps

摘要

We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms,and identify various interesting features as a function of two control parameters.In particular,we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1,period-2,and period-3 orbits.We also investigate the multistability in the same coupling.Lyapunov exponents,parameter planes,phase space portraits,and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states,from quasiperiodic to mode-locked states and to chaotic states,and from chaotic to hyperchaotic states.