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Coupled stochastic systems of Skorokhod type: Well-posedness of a mathematical model and its applications
Wilfrid Laurier University, Canada.ORCID iD: 0000-0002-3873-2245
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
Wilfrid Laurier University, Canada; BCAM—Basque Center for Applied Mathematics, Spain.
2023 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 46, no 6, p. 7368-7390Article in journal (Refereed) Published
Abstract [en]

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 modeling 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, modeling 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.

Place, publisher, year, edition, pages
John Wiley & Sons, 2023. Vol. 46, no 6, p. 7368-7390
Keywords [en]
compound Poisson process, excitatory neurons, finite activity jumps, inhibitory neurons, population dynamics, reflecting boundary condition, Skorokhod equations, stochastic differential equations, well-posedness, Wilson-Cowan equations
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-93020DOI: 10.1002/mma.8975ISI: 000905516000001Scopus ID: 2-s2.0-85145277197OAI: oai:DiVA.org:kau-93020DiVA, id: diva2:1729798
Available from: 2023-01-23 Created: 2023-01-23 Last updated: 2023-04-17Bibliographically approved

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Muntean, Adrian

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