Analysis of Periodic Orbits for the Chen and the Lü Systems via a Variational Approach

In this research, we systematically investigated the organization of the unstable cycles for the Chen and the Lü systems. The multivalued and non-invertible return maps show the complexity of the two dissipative flows, and a new designed method for building one-dimensional symbolic dynamics based on the orbital topological structure is proposed. We employed the variational approach for the calculations of unstable periodic orbits and used two orbital fragments for initialization. The homotopy evolution of periodic orbits provides evolution rules for the periods. For a chaotic flow, current work supplies an interesting framework for a chart of periodic orbits.