Electron. J. Differential Equations, Vol. 2020 (2020), No. 86, pp. 1-18.

Dynamics of a diffusive competitive model on a periodically evolving domain

Jiazhen Zhu, Jiazheng Zhou, Zhigui Lin

This article concerns a two-species competitive model with diffusive terms in a periodically evolving domain and study the impact of the spatial periodic evolution on the dynamics of the model. The Lagrangian transformation approach is adopted to convert the model from a changing domain to a fixed domain with the assumption that the evolution of habitat is uniform and isotropic. The ecological reproduction indexes of the linearized model are given as thresholds to reveal the dynamic behavior of the competitive model. Our theoretical results show that a lager evolving rate benefits the persistence of competitive populations for both sides in the long run. Numerical experiments illustrate that two competitive species, one of which survive and the other vanish in a fixed domain, both survive in a domain with a large evolving rate, and both vanish in a domain with a small evolving rate.

Submitted May 9, 2019. Published August 1, 2020.
Math Subject Classifications: 35K57, 35K55, 92D25.
Key Words: Competitive model; diffusion; evolving domain; ecological reproduction indexes.
DOI: 10.58997/ejde.2020.86

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Jiazhen Zhu
School of Mathematical Science
Yangzhou University
Yangzhou 225002, China
email: luckyjiazhenzhu@foxmail.com
Jiazheng Zhou
Departamento de Matemática
Universidade de Brasília, BR 70910-900
Brasília-DF, Brazil
email: zhoumat@hotmail.com, zhou@mat.unb.br
Zhigui Lin
School of Mathematical Science
Yangzhou University
Yangzhou 225002, China
email: zglin68@hotmail.com, zglin@yzu.edu.cn

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