Qualitative Analysis of a Three-Species Reaction-Diffusion Model with Modified Leslie-Gower Scheme | Zendy

Xiaoni Wang | Zendy; Gaihui Guo | Zendy; Jian Li | Zendy; Mengmeng Du | Zendy

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Qualitative Analysis of a Three-Species Reaction-Diffusion Model with Modified Leslie-Gower Scheme

Author(s) -

Xiaoni Wang,

Gaihui Guo,

Jian Li,

Mengmeng Du

Publication year - 2021

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 28

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2021/6650783

Subject(s) - mathematics , ode , reaction–diffusion system , neumann boundary condition , mathematical analysis , a priori and a posteriori , stability (learning theory) , maximum principle , diffusion , harnack's inequality , constant (computer programming) , boundary (topology) , physics , mathematical optimization , thermodynamics , computer science , philosophy , epistemology , machine learning , optimal control , programming language

The qualitative analysis of a three-species reaction-diffusion model with a modified Leslie-Gower scheme under the Neumann boundary condition is obtained. The existence and the stability of the constant solutions for the ODE system and PDE system are discussed, respectively. And then, the priori estimates of positive steady states are given by the maximum principle and Harnack inequality. Moreover, the nonexistence of nonconstant positive steady states is derived by using Poincaré inequality. Finally, the existence of nonconstant positive steady states is established based on the Leray-Schauder degree theory.

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