Convergence and stability analysis of system of partial differential equations under Markovian structural perturbations–ii:vextor Lyapunov–like functionals

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In this paper we employ the theory of dererministic ordinary differential inequalities together with the concept of vector Lyapunov–like functional to develop basic comparison theorems for system of partial differential equations of parabolic type under Markovian structural perturbations.These results will be utilized to give sufficient conditions for the convergence and stability of the solution process of the system.We also characterize the effects of the random structural perturbations on the qualitative properties of such system. Moreover,the Lyapunov–like functional approach provides a mechanism to characterize the diffusion effects on the qualitative properties of the system.