Hopf bifurcation, dynamics at infinity and robust modified function projective synchronization (RMFPS) problem for Sprott E system with quadratic perturbation were studied in this paper. By using the method of projection for center manifold computation, the subcritical and the supercritical Hopf bifurcation were analyzed and obtained. Then, in accordance with the Poincare compactification of polynomial vector field in R3, the dynamical behaviors at infinity were described completely. Moreover, a RMFPS scheme of this special system was proposed and proved based on Lyapunov direct method. The simulation results demonstrate the correctness of the dynamics analysis and the effectiveness of the proposed synchronization strategy.
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.