Global Attractivitv And Existence Of Periodic Solution For Two Kind Of Stochastic Nonautonomous ODEs

In the natural science,engineering technology.econoimic management.biochemistry.the dynamics of the financial process.etc.,there are many practical problems correspond-ing to the mathematical model is a stochastic differential equation.In the last few decades,many scholars have done a lot of research on many aspects of stochastic differential equa-tions,such as,the existence and uniqueness,global attractivity.stability and asymptotic behavior,the numerical solution,and so on.However.There are few articles on periodic solutions and global attractivity for stochastic nonautonomous differential equations.In this paper,we study the existence of periodic solutions and global attractivity for two kinds of stochastic nonautonomous differential equations,where,in the second chapter.we considered periodic solution for a stochastic nonautonomous HIV-1 model with logistic target cell growthIn the third chapter,we considered global attractivity of stochastic non-autonomous toxic-producing phytoplankton allelopathy modelwhere,B(t):Bi(t)is a standarcd Brownian motion.?(t),?(t)represents the intensity of the Gaussian white noise.These two kinds of equations are stochastic non-autonomous differential equation-s.By using Ito formula,constructing the Lyapunov function,the expected inequality,the differential inequality technique and some analysis methods.Through rigorous proof,we find the sufficient conditions for the periodic solutions and the global attractivity of the two kinds of differential equations,and some applications are presented for the established results.