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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

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Adrian Muntean
Karlstads Universitet
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Roderick Melnik
Wilfrid Laurier University
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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