Large-scale stochastic hereditary systems under Markovian structural perturbations. Part III. Qualitative analysis

Abstract

In this final part of the work, the convergence and stability analysis of large-scale stochastic hereditary systems under random structural perturbations is investigated. This is achieved through the development and the utilization of comparison theorems in the context of vector Lyapunov-like functions and decomposition-aggregation method. The byproduct of the investigation suggests that the qualitative properties of decoupled stochastic hereditary subsystems under random structural perturbations are preserved, as long as the self-inhibitory effects of subsystems are larger than cross-interaction effects of the subsystems. Again, it is shown that these properties are affected by hereditary and random structural perturbations effects. It is further shown that the mathematical conditions are algebraically simple, and are robust to the parametric changes. Moreover, the work generates a concept of block quasimonotone nondecreasing property that is useful for the investigation of hierarchic systems. These results are further extended to the integrodifferential equations of Fredholm type.