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Spatial pattern formation and delay induced destabilization in predator-prey model with fear effect
  • Swati Mishra,
Swati Mishra
Indian Institute of Technology (Indian School of Mines) Dhanbad

Corresponding Author:[email protected]

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Indian Institute of Technology (Indian School of Mines) Dhanbad
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Recent field experiments showed that predators influence the prey population not only by direct consumption but also by stimulating various defensive strategies. The cost of these defensive strategies can include energetic investment in defensive structures, reduced energy income, lower mating success, and emigration which ultimately reduces the reproduction of prey. To explore the effect of these defensive strategies (anti-predator behaviors), a modified Leslie-Gower predator-prey model with the cost of fear has been considered. Gestation delay is also incorporated in the system for a more realistic formulation. Boundedness, equilibria and stability analysis of the temporal model are studied. By considering gestation delay as a bifurcation parameter, the existence of Hopf-bifurcation around the interior equilibrium point is discussed together with the direction, stability and period of bifurcating solutions arising through Hopf-bifurcation. The spatial extension of the proposed model incorporating density-dependent cross-diffusion is also investigated and the conditions for diffusion-driven instability are obtained. To illustrate the analytical findings, detailed numerical simulations are performed. Biologically realistic Turing patterns as hexagonal spots, spots and stripes mixture, and labyrinthine type patterns are identified. It is found that the fear level has a stabilizing impact on delay induced destabilization and both stabilizing and destabilizing effects on Turing instability.
19 May 2021Submitted to Mathematical Methods in the Applied Sciences
20 May 2021Submission Checks Completed
20 May 2021Assigned to Editor
22 May 2021Reviewer(s) Assigned
27 Sep 2021Review(s) Completed, Editorial Evaluation Pending
27 Sep 2021Editorial Decision: Revise Major
18 Oct 20211st Revision Received
18 Oct 2021Submission Checks Completed
18 Oct 2021Assigned to Editor
21 Oct 2021Reviewer(s) Assigned
15 Nov 2021Review(s) Completed, Editorial Evaluation Pending
30 Dec 2021Editorial Decision: Revise Major
24 Jan 20222nd Revision Received
25 Jan 2022Submission Checks Completed
25 Jan 2022Assigned to Editor
25 Jan 2022Reviewer(s) Assigned
26 Jan 2022Review(s) Completed, Editorial Evaluation Pending
09 Feb 2022Editorial Decision: Accept
30 Jul 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 11 on pages 6801-6823. 10.1002/mma.8207