Stable spatially inhomogeneous periodic solutions for a diffusive Leslie–Gower predator–prey model

The main objective of this thesis is to learn about the dynamics of a diffusive Leslie–Gower predator–prey system with functional response and time delay under homogeneous Neumann boundary conditions. By in-depth analyzing eigenvalues distribution, it proves that there are (diffusion-induced, delay-...

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Bibliographic Details
Published inJournal of applied mathematics & computing Vol. 70; no. 3; pp. 2541 - 2567
Main Author Jiang, Heping
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Subjects
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Theory of Computation
Predator–prey model
Spatially inhomogeneous periodic solutions
Time delay
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Summary:The main objective of this thesis is to learn about the dynamics of a diffusive Leslie–Gower predator–prey system with functional response and time delay under homogeneous Neumann boundary conditions. By in-depth analyzing eigenvalues distribution, it proves that there are (diffusion-induced, delay-induced) Turing–Hopf bifurcations around positive equilibrium state. More than this, base on the foundation of the regular modality and the center manifold theory, It is responsible for establishing a precise formula, which is to determine the Turing–Hopf bifurcation property of a diffusive Leslie–Gower predator–prey system with functional response. After that, we applied the formula to a diffusive Leslie–Gower predator–prey system with Beddington–DeAngelis functional response and time delay integrally. Finally, the results have been verified and replenished by numerical simulation adequately.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02018-2