Stability Analysis Of Two Types Of Nonlinear Dynamic Systems

In this paper,two nonlinear systems are studied.Based on Lyapunov stability theo-ry,then we can use the Mawhin Continuation Theorem to prove the asymptotic stability of the periodic solution of a kind of predator-prey system.By using mean value theorem of integrals,Banach's fixed point theorem and other methods,Mittag-Leffler stability of a kind of fraction-order neural network model is investigated.The narrative structure of the article is arranged as follows:The first chapter introduces the predator-prey model and fraction-order neural net-work models' research background,research status and common research methods.The second chapter mainly studies some properties of a predator-prey system with generalized Holling type III functional response.Based on Mawhin's Continuation The-orem,some sufficient conditions for the existence of periodic solutions are obtained.Moreover,the global stability of the periodic solution is built with the help of a suitable Lyapunov functionIn the third chapter,a kind of fraction-order neural network with time-varying delay is studied.By mean value theorem of integrals,inequality technique and Banach fixed point theorem,the Mittag-leffler stability of the unique solution of the system can be proved when some conditions are satisfied.