Controlling Hamiltonian chaos by medium perturbation in periodically driven systems

Abstract

By employing another external field with intensity not larger than 60% of the original driving force, the Hamiltonian chaos in a driven Morse oscillator could be controlled in the sense that the bound state regions can be changed at will. Based on our understanding about the complex dynamics of a periodically driven Hamiltonian system with one degree of freedom by two external fields, an idea of decreasing bound regions is proposed. A formula for island width, being helpful for selecting a proper controlling field, is derived. The mechanism in increasing bound regions extracted from a large number of numerical experiments is still not so clear at present, but we have gotten a good grasp of the roles of controlling parameters with suppression of Hamiltonian chaos. Though no small perturbations with this method can have a satisfactory effect, as previous studies, some remarks about the magnitude of perturbation are presented.