Journal
JOURNAL OF BIOLOGICAL DYNAMICS
Volume 14, Issue 1, Pages 826-848Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17513758.2020.1850892
Keywords
Schooling behaviour; time delay; Hopf bifurcation; Predator– prey; Allee effect
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Funding
- National Natural Science Foundation of China [11661050,11860014]
- HongLiu First-class Disciplines Development Program of Lanzhou University of Technology
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In this paper, a delayed diffusive predator-prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results.
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