Narrow Results

In this paper, the systematical calculations of the unstable cycles for the Burke–Shaw system (BSS) are presented. In contrast to the Poincaré section method used in previous studies, we used the variational method for the cycle search and established appropriate symbolic dynamics on the basis of the topological structure of the cycles. The variational approach made it easy to continuously track the periodic orbits when the parameters were varied. Structure of the whole cycle in the dissipative system demonstrated that the methodology could be effective in most low-dimensional chaotic systems.