Stochastic partial differential equation models for spatially dependent predator-prey equations

Nhu N. Nguyen; George Yin

doi:10.3934/dcdsb.2019175

Article Contents

2020, Volume 25, Issue 1: 117-139. Doi: 10.3934/dcdsb.2019175

This issue Previous Article Detailed analytic study of the compact pairwise model for SIS epidemic propagation on networks Next Article Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries

Stochastic partial differential equation models for spatially dependent predator-prey equations

Nhu N. Nguyen and
George Yin

Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

Received: November 2018

Revised: March 2019

Early access: July 2019

Published: January 2020

This research was supported in part by the National Science Foundation under grant DMS-1710827.

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Abstract

Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE models are more versatile. To incorporate more qualitative features of the ratio-dependent models, the Beddington-DeAngelis functional response is also used. To analyze the systems under consideration, first existence and uniqueness of solutions of the SPDEs are obtained using the notion of mild solutions. Then sufficient conditions for permanence and extinction are derived.

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Mathematics Subject Classification: Primary: 60H15, 92D25, 92D40, 35Q92.

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