Heteroclinic Cycles in a Competitive Network

Abstract

The competitive threshold linear networks have been recently developed and are typical examples of nonsmooth systems that can be easily constructed. Due to their flexibility for manipulation, they are used in several applications, but their dynamics (both local and global) are not completely understood. In this work, we take some recently developed threshold systems and by a simple modification in the parameter space, we obtain new global dynamic behavior. Heteroclinic cycles and other remarkable scenarios of global bifurcation are reported.

Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems

“…Carmona et al [9,8,7] investigated "T-point"heteroclinic cycles and homoclinic cycles in a piecewise linear version of Michelson system. Chialva and Reartes [12] obtained that a piecewise linear system has a heteroclinic cycle by modifying parameter space. Yang et al [37,34,35,31,32] studied the existence conditions for homoclinic orbits and heteroclinic cycles in some piecewise linear systems with two zones.…”