Affiliation:
1. School of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
2. Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Abstract
In this paper, we propose a diffusive predator–prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. We mainly study the local stability of the coexisting equilibrium and the existence and properties of Hopf bifurcation. We provide bifurcation diagrams with the fear effect parameter (s) and the Allee effect parameter (a), showing that the stable region of the coexisting equilibrium increases (or decreases) with an increase in the fear effect parameter (s) (or the Allee effect parameter (a)). We also show that gestation delay (τ) can affect the local stability of the coexisting equilibrium. When the delay (τ) is greater than the critical value, the coexistence equilibrium loses its stability, and bifurcating periodic solutions appear. Whether the bifurcated periodic solution is spatially homogeneous or inhomogeneous depends on the fear effect parameter (s) and the Allee effect parameter (a). These results show that the fear effect parameter (s), the Allee effect parameter (a), and gestation delay (τ) can be used to control the growth of prey and predator populations.
Funder
Fundamental Research Funds for the Central Universities
Harbin Science and Technology Bureau Manufacturing Innovation Talent Project
Heilongjiang Science and Technology Department Provincial Key R&D Program Applied Research Project
Heilongjiang Science and Technology Department Provincial Key R&D Program Guidance Project
Postdoctoral program of Heilongjiang Province
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
2 articles.
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