Zhang X, Zhao H. Dynamics analysis of a delayed reaction-diffusion predator-prey system with non-continuous threshold harvesting.
Math Biosci 2017;
289:130-141. [PMID:
28529143 DOI:
10.1016/j.mbs.2017.05.007]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2016] [Revised: 04/09/2017] [Accepted: 05/17/2017] [Indexed: 10/19/2022]
Abstract
This paper deals with a delayed reaction-diffusion predator-prey model with non-continuous threshold harvesting. Sufficient conditions for the local stability of the regular equilibrium, the existence of Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation. By utilizing upper-lower solution method and Lyapunov functions the globally asymptotically stability of a unique regular equilibrium and asymptotically stability of a unique pseudoequilibrium are studied respectively. Further, the boundary node bifurcations are studied. Finally, numerical simulation results are presented to validate the theoretical analysis.
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