In this paper, we consider a three-unit delayed neural network system, investigate the linear stability, and obtain some sufficient conditions ensuring the absolute synchronization of the system by the Lyapunov function. Numerical simulations show that the theoretically predicted results are in excellent agreement with the numerically observed behavior.
In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed by bifurcation theory of impulsive differential equation. Finally, the analytical results presented in the work are validated by numerical simulation figures for this proposed model.