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Population dynamics with complex biological interactions, accounting foruncertainty quantification, is critical for many application areas. However,due to the complexity of biological systems, the mathematical formulation ofthe corresponding problems faces the challenge that the correspondingstochastic processes should, in most cases, be considered in bounded domains.We propose a model based on a coupled system of reflecting Skorokhod-typestochastic differential equations with jump-like exit from a boundary. Thesetting describes the population dynamics of active and passive populations. Asmain working techniques, we use compactness methods and Skorokhod'srepresentation of solutions to SDEs posed in bounded domains to prove thewell-posedness of the system. This functional setting is a new point of view inthe field of modelling and simulation of population dynamics. We provide thedetails of the model, as well as representative numerical examples, and discussthe applications of a Wilson-Cowan-type system, modelling the dynamics of twointeracting populations of excitatory and inhibitory neurons. Furthermore, thepresence of random input current, reflecting factors together with Poissonjumps, increases firing activity in neuronal systems.

Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications