Bifurcation and Number of Periodic Solutions of Some 2n-Dimensional Systems and Its Application

In high dimension, the bifurcation theory of periodic orbits of nonlinear dynamics systems are difficult to establish in general. In this paper, by performing the curvilinear coordinate frame and constructing a Poincare map, we obtain some sufficient conditions of the bifurcation of periodic solutions of some 2n-dimensional systems for the unperturbed system in two cases: one is a decoupled n-degree-of-freedom nonlinear Hamiltonian system and the other has an isolated invariant torus. We use a new method and study new types of systems compared with the existing results. As an application we study the bifurcation and number of periodic solutions of an ice covered suspension system. Under a certain parametrical condition, the number of periodic solutions of this system can be 2 or 1 with the variation of parameter $$p_{2}$$ .