| Issue |
Math. Model. Nat. Phenom.
Volume 19, 2024
|
|
|---|---|---|
| Article Number | 5 | |
| Number of page(s) | 31 | |
| Section | Population dynamics and epidemiology | |
| DOI | https://doi.org/10.1051/mmnp/2024003 | |
| Published online | 22 March 2024 | |
Global Hopf Bifurcation Of a Delayed Diffusive Gause-Type Predator-Prey System with the Fear Effect and Holling Type III Functional Response
1
Department of Mathematics, Northeast Forestry University,
Harbin,
Heilongjiang
150040,
PR China
2
Engineering Research Center of Agricultural Microbiology Technology, Ministry of Education & Heilongjiang Provincial Key Laboratory of Ecological Restoration and Resource Utilization for Cold Region & School of Mathematical Science, Heilongjiang University,
Harbin
150080,
PR China
* Corresponding author: liuming_girl@163.com
Received:
23
June
2023
Accepted:
7
February
2024
In this paper, a delayed diffusive predator-prey system with the fear effect and Holling type III functional response is considered, and Neumann boundary condition is imposed on this system. First, we explore the stability of the unique positive constant steady state and the existence of local Hopf bifurcation. Then the global attraction domain G* of system (1.4) is obtained by the comparison principle and the iterative method. Through constructing the Lyapunov function, we investigate uniform boundedness of periodic solutions' periods. Finally, we prove the global continuation of periodic solutions by the global Hopf bifurcation theorem of Wu. Moreover, some numerical simulations that support the analysis results are given.
Mathematics Subject Classification: 35A01 / 35B10 / 35B32 / 37G15
Key words: Gause-type predator—prey system / fear effect / time delay / diffusion / global Hopf bifurcation
© The authors. Published by EDP Sciences, 2024
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