COMPLEX DYNAMICS OF A HAMILTONIAN SYSTEM UNDER IMPULSIVE CONTROL

Abstract

In this paper, the dynamical behavior of a Hamiltonian system under impulsive control is discussed by both theoretical and numerical analyses. The existence and stability of its period-one and period-three solutions are obtained in virtue of a discrete map. The conditions of existence for flip bifurcation and Hopf bifurcation are further derived by using center manifold theorem and bifurcation theory. Three attracting invariant closed curves, surrounding three fixed points respectively, are investigated. Moreover, chaos in the sense of Marotto is rigorously proven. Finally, some detailed numerical results including periodic solutions, bifurcation diagrams, and chaotic attractors, are illustrated by examples, which are in good agreement with the theoretical analysis.