Kybernetika 53 no. 2, 354-369, 2017

Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

Zhen Wang, Wei Sun, Zhouchao Wei and Shanwen ZhangDOI: 10.14736/kyb-2017-2-0354


Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics at infinity of this system are analyzed through Poincaré compactification. The simulation results demonstrate feasibility of periodic parametric perturbation control technology and correctness of the theoretical results.


Hamiltonian system, homoclinic orbits, Melnikov's methods, periodic orbits, periodic parametric perturbation, dynamics at infinity


34H10, 34D20, 34H20


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