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