Affiliation:
1. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, P. R. China
Abstract
In this paper, bifurcations of heterodimensional cycle with one nonhyperbolic equilibrium and one saddle-focus in three-dimensional vector fields are investigated. We study the interaction of a transcritical bifurcation with a codimension-0/codimension-2 heteroclinic cycle. Based on the construction of a Poincaré return map, we obtain the expressions of parametric curves of homoclinic and heteroclinic connections around the heterodimensional cycle as well as periodic orbits. Furthermore, the configurations of the parametric curves corresponding to different bifurcations are illustrated.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)