Bifurcation and number of subharmonic solutions of a 2n-dimensional non-autonomous system and its application

Abstract

This paper is devoted to consider the existence and bifurcation of subharmonic solutions of two types of 2n-dimensional nonlinear systems with time-dependent perturbations. When the unperturbed system is a Hamiltonian system, we obtain the extended Melnikov function by means of performing the curvilinear coordinate frame and constructing a Poincare map. Then some conditions of the bifurcation of subharmonic solutions are obtained. The results obtained in this paper contain and improve the existing results for $$n=2,3$$ . When the unperturbed system contains an isolated invariant torus, we investigate the bifurcation of subharmonic solutions by analyzing the Poincare map. We apply the extended Melnikov method to study the bifurcation and number of subharmonic solutions of the ice-covered suspension system. The maximum number of subharmonic solutions of this system is 2, and the relative parameter control condition is obtained.