Electron. J. Differential Equations, Vol. 2025 (2025), No. 38, pp. 1-19.
Traveling waves of a diffusive modified Leslie-Gower model with chemotaxis
Shuna Wang, Jiang Liu, Jun Fang, Xiaojie Lin
Abstract:
In this article, we study a diffusive modified Leslie-Gower model with
chemotaxis and large wave speed. By applying traveling wave transformation
and changing the time scale, this modified Leslie-Gower model can be
transformed into a singularly perturbed system. We establish the existence
of heteroclinic orbits connecting different equilibria for the system without
perturbation by constructing invariant regions and using the
Poincare-Bendixson theorem. Then the existence of traveling wave
solutions for the diffusive modified Leslie-Gower system is demonstrated
via the geometric singular perturbation theory and Fredholm theory.
Submitted February 21, 2025. Published April 10, 2025.
Math Subject Classifications: 35K57, 92D25, 35C07, 34D15.
Key Words: Modified Leslie-Gower model; chemotaxis; traveling waves; geometric singular perturbation.
DOI: 10.58997/ejde.2025.38
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Shuna Wang
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: 2020211141@jsnu.edu.cn
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Jiang Liu
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: jiangliu@jsnu.edu.cn
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Jun Fang
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: 2020231222@jsnu.edu.cn
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Xiaojie Lin
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: linxiaojie@jsnu.edu.cn
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