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Using the combination of qualitative analysis and numerical calculation, the limit cycle number and stability of the two mechanical systems are discussed. First of all, the limit cycles of the class of 2-order Hamiltonian functions are obtained by Melnikov bifurcation method. The system has four limit periods under three perturbations, three of which are generated near the homoclinic orbit. Then, the periodic vibration of the neural network model with non autonomous pulse delay is discussed. This pulse is differentiated by the principle of solution equivalence, and its equation is transformed into a continuous system. The existence and uniqueness of periodic solutions and exponential stability are obtained by using matrix spectrum theory and analytic inequality.

Study and Analysis of Limit Cycle Bifurcation and Stability of Two Kinds of Dynamical Systems