Two-species competing population dynamics with the population-dependent environmental capacities under random disturbance

Yoshioka, Hidekazu

doi:10.1007/s12064-020-00321-7

Original Article
Published: 11 August 2020

Two-species competing population dynamics with the population-dependent environmental capacities under random disturbance

Hidekazu Yoshioka ORCID: orcid.org/0000-0002-5293-3246¹

Theory in Biosciences volume 139, pages 279–297 (2020)Cite this article

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Abstract

We propose and analyze a stochastic competing two-species population dynamics model subject to jump and continuous correlated noises. Competing benthic algae population dynamics in river environment, which is an important engineering problem, motivates this new model. The model is a system of stochastic differential equations having a characteristic that the two populations are competing with each other through the environmental capacities; an increase in one population decreases the other’s environmental capacity. Unique existence of the uniformly bounded strong solution is proven, and attractors of the solutions are identified depending on the parameter values. The Kolmogorov’s backward equation associated with the population dynamics is formulated and its unique solvability in a Banach space with a weighted norm is discussed. A novel uncertain correlation case is also analyzed in the framework of viscosity solutions. Numerical computation results using a finite difference scheme and a Monte-Carlo method are presented to deeper analyze the model. Our analysis results can be utilized for establishment of a foundation for modeling, analysis and control of the competing population dynamics.

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Acknowledgements

Kurita Water and Environment Foundation Grant No. 19B018, and a grant for ecological survey of a life history of the landlocked ayu Plecoglossus altivelis altivelis from the Ministry of Land, Infrastructure, Transport and Tourism of Japan support this research. This research was carried out under a support of the research fund for young researchers in Shimane University.

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Graduate School of Natural Science and Technology, Shimane University, Nishikawatsu-cho 1060, Matsue, 690-8504, Japan
Hidekazu Yoshioka

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Yoshioka, H. Two-species competing population dynamics with the population-dependent environmental capacities under random disturbance. Theory Biosci. 139, 279–297 (2020). https://doi.org/10.1007/s12064-020-00321-7

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Received: 27 March 2020
Accepted: 01 August 2020
Published: 11 August 2020
Issue Date: September 2020
DOI: https://doi.org/10.1007/s12064-020-00321-7

Keywords

River environment
Algae bloom
Stochastic differential equation
Population-dependent environmental capacity
Kolmogorov’s backward equation
Weak solutions