Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey

Prabir Panja; Soovoojeet Jana; Shyamal kumar Mondal

doi:10.3934/naco.2020033

Article Contents

2021, Volume 11, Issue 3: 391-405. Doi: 10.3934/naco.2020033

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Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey

1.
Department of Applied Science, Haldia Institute of Technology, Haldia-721657, W. B., India
2.
Department of Mathematics, Ramsaday College, Amta, Howrah, India
3.
Department of Applied Mathematics with Oceanology, and Computer Programming, Vidyasagar University, Midnapore -721102, W. B., India

^* Corresponding author: Prabir Panja, prabirpanja@gmail.com
^* Corresponding author: Prabir Panja, prabirpanja@gmail.com

Received: February 2020

Revised: February 2020

Early access: May 2020

Published: September 2021

Abstract / Introduction Full Text(HTML) Figure(8) Related Papers Cited by

Abstract

In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic. Global dynamics of the co-existing equilibrium point has been discussed with the help of the geometric approach. Furthermore, it is established that the proposed system undergoes through a Hopf bifurcation with respect to some important parameters. Finally, some numerical simulations have been done to test our theoretical results.

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Mathematics Subject Classification: Primary: 92B05, 92D25; Secondary: 92D40.

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Figure 1. Local stability of the equilibrium point $ E_1 $

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Figure 2. Local stability of the equilibrium point $ E^{*} $

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Figure 3. Global stability of interior equilibrium

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Figure 4. Bifurcation diagram of system $ (1) $ with respect to $ \eta $

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Figure 5. Bifurcation diagram of system $ (1) $ with respect to $ \beta $

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Figure 6. Bifurcation diagram of system $ (1) $ with respect to $ \beta_1 $

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Figure 7. Bifurcation diagram of system $ (1) $ with respect to $ \beta_2 $

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Figure 8. Bifurcation diagram of system $ (1) $ with respect to $ \gamma $

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