Bifurcation and number of subharmonic solutions of a 4D non-autonomous slow–fast system and its application

• DOI: 10.1007/s11071-018-4086-4
• Publication Date: 2018-01-31T14:20:13Z
• Authors: Jing Li; Tingting Quan; Wei Zhang
• Keywords: Subharmonic; Bogdanov–Takens bifurcation

In this paper, we study the existence and bifurcation of subharmonic solutions of a four-dimensional slow–fast system with time-dependent perturbations for the unperturbed system in two cases: one is a Hamilton system and the other has a singular periodic orbit, respectively. We perform the curvilinear coordinate transformation and construct a Poincare map for both cases. Then some of sufficient conditions and necessary conditions of the existence and bifurcation of subharmonic solutions are obtained by analyzing the Poincare map. We apply them to study the bifurcation of multiple subharmonic solutions of a honeycomb sandwich plate dynamics system and to discuss the number of subharmonic solutions in different bifurcation regions induced by two parameters. The maximum number of subharmonic solutions of the honeycomb sandwich plate system is 7 and the relative parameter control condition is obtained.