Coupled stochastic systems of Skorokhod type: well-posedness of a
mathematical model and its applications
- Thoa Thieu,
- Adrian Muntean,
- Roderick Melnik
Thoa Thieu
Wilfrid Laurier University
Corresponding Author:tthieu@wlu.ca
Author ProfileAbstract
Population dynamics with complex biological interactions, accounting for
uncertainty quantification, are critical for many application areas.
However, due to the complexity of biological systems, the mathematical
formulation of the corresponding problems faces the challenge that the
corresponding stochastic processes should, in most cases, be considered
in bounded domains. We propose a model based on a coupled system of
reflecting Skorokhod-type stochastic differential equations with
jump-like exit from a boundary. The setting describes the population
dynamics of active and passive populations. As main working techniques,
we use compactness methods and Skorokhod's representation of solutions
to SDEs posed in bounded domains to prove the well-posedness of the
system. This functional setting is a new point of view in the field of
modelling and simulation of population dynamics. We provide the details
of the model, as well as representative numerical examples, and discuss
the applications of a Wilson-Cowan-type system, modelling the dynamics
of two interacting populations of excitatory and inhibitory neurons.
Furthermore, the presence of random input current, reflecting factors
together with Poisson jumps, increases firing activity in neuronal
systems.03 Aug 2022Submitted to Mathematical Methods in the Applied Sciences 05 Aug 2022Submission Checks Completed
05 Aug 2022Assigned to Editor
12 Aug 2022Reviewer(s) Assigned
24 Nov 2022Review(s) Completed, Editorial Evaluation Pending
25 Nov 2022Editorial Decision: Revise Minor
06 Dec 20221st Revision Received
07 Dec 2022Submission Checks Completed
07 Dec 2022Assigned to Editor
07 Dec 2022Review(s) Completed, Editorial Evaluation Pending
07 Dec 2022Reviewer(s) Assigned
07 Dec 2022Editorial Decision: Accept