Journal
NONLINEAR DYNAMICS
Volume 78, Issue 1, Pages 505-523Publisher
SPRINGER
DOI: 10.1007/s11071-014-1457-3
Keywords
Modified Leslie-Gower type growth; Strong Allee effect; Persistence; Multiple delay; Hopf bifurcation; Global stability
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This paper describes a multiple delayed modified Leslie-Gower type predator-prey system with a strong Allee effect in prey population growth. Non-selective effort is used to harvest the population. The dynamical characteristics of the delay induced system are rigorously studied using mathematical tools. The existence of coexistence equilibria is ensured, and the dynamic behavior of the system is investigated around coexistence equilibria. Uniform strong persistence and permanence of the system are discussed in order to ensure long-term survival of the species. The stability of the delay preserved system is investigated. Sufficient conditions are derived for local and global stability of the system. The existence of Hopf bifurcation phenomenon is examined around interior equilibria of the system. Subsequently, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. Finally, numerical simulations are carried out to validate the analytical findings.
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