Stability of General Systems in Biological, Physical and Social Sciences
The systems of nonlinear differential equations represent the mathematical model of several general systems in biological, physical and social sciences . One of the most versatile techniques in the theory of nonlinear differential systems is the second method of Lyapunov [1,2]. The notion of vector Lyapunov functions, together with the theory of systems of differential inequalities, provides a very general comparison principle by means of which a number of qualitative properties of solutions of deterministic functional differential systems are studied in a unified way . It is natural to expect such an extension to stochastic functional differential systems. The obtained comparison principles to stochastic functional differential systems have been utilized to study the stability behavior of hereditary stochastic general systems.
KeywordsFunctional Differential Equation Differential Inequality Stochastic Functional Differential Equation Vector Lyapunov Function Hereditary System
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