Analysis On Dynamic Behavior Of Several Class Of Stochastic Differential Equations

In recent years,the theories of stochastic differential equations have been widely used in ecology,systems science,artificial intelligence,chemical engineering,medicine,finance and other fields,and have attracted more and more attentions of scholars at home and abroad.In the field of ecology,studying the dynamic relationship between predator and prey can help people take effective measures to manage biological populations in nature.which has very important significance.Artificial neural networks are information processing systems,have the same characteristics as biological neural networks and have a wide range of applications in related fields such as artificial intelligence,pattern recognition and image processing.Therefore,both the biological population model and the neural network model are worthy of our in-depth study.On one hand,we investigate the dynamics of a stochastic predator-prey system with modified Leslie-Gower and Holling-type ? schemes,and the existence and uniqueness of the solution are obtained.Then,by constructing the auxiliary function and applying some inequality techniques,we obtain the random persistence of the system.By constructing appropriate Lyapunov functions and applying Ito's formula,the time average persistence and extinction of stochastic system are studied.Moreover,under certain parametric restrictions,we obtain that the system has a stationary distribution which is ergodic.Finally.some numerical simulations are carried out to support our results.On the other hand,we add stochastic perturbations and Markovian switching into the fuzzy Cohen-Grossberg neural networks with time delays and obtain a more realistic model.Additionally,some novel sufficient criteria of exponential synchronization are also derived by utilizing Lyapunov method and graph theory.Ultimately,a numerical example is provided to illustrate the effectiveness and feasibility of the theoretical results.