Bifurcations Of Limit Cycles And Stability Analysis Of Two Classes Of Dynamical Systems

In this paper, we discuss the number of limit cycles and stability of two classes of dynamical systems using qualitative analysis and numerical computing. First, we discuss the number of limit cycles of a cubic near-Hamiltonian system under cubic perturbations. By using the Melnikov bifurcation method, we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop. Second, through the solution principle of equivalence of the impulse differential equation and the continuous system, we reduce the impulse differential equation to the continuous system. By the M-matrix, the spectrum theory and analysis inequality methods and so on, we obtain existence, uniqueness and global exponential stability of the periodic solution, improving the some known results [33, 43].This paper consists of three chapters. We describe them briefly one by one.In chapter 1, we outline the research advance and some concept of dynamical systems. We also introduce our main results.In chapter 2, we study the number of limit cycles of a cubic near-Hamiltonian system under cubic perturbations.In chapter 3, we mainly concern with periodic oscillation for non-autonomous BAM neural networks with impulses.