Chaos inducement and Enhancement in Two Particular Nonlinear Maps Using Weak Periodic/quasiperiodic Perturbations

Weak periodic perturbation has long been used to suppress chaos in dynamical systems. In this paper, however, we demonstrate that weak periodic or quasiperiodic perturbation can also be used to induce chaos in nonchaotic parameter ranges of chaotic maps, or to enhance the already existing chaotic state. Two kinds of chaotic maps, the period doubling system and the Hopf bifurcation system, are employed as basic models to analyze and compare in detail the different mechanisms of inducing and enhancing chaos in them. In addition, a special kind of intermittency characterized by its periodicity is found for the first time in periodically perturbed Henon map, and reasonable speculations are presented to explain its complicated dynamics.