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Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge

  • Sudeshna Mondal and Guruprasad Samanta EMAIL logo
Published/Copyright: September 28, 2020
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 1

Abstract

A field experiment on terrestrial vertebrates observes that direct predation on predator–prey interaction can not only affect the population dynamics but the indirect effect of predator’s fear (felt by prey) through chemical and/or vocal cues may also reduce the reproduction of prey and change their life history. In this work, we have described a predator–prey model with Holling type II functional response incorporating prey refuge. Irrespective of being considering either a constant number of prey being refuged or a proportion of the prey population being refuged, a different growth rate and different carrying capacity for the prey population in the refuge area are considered. The total prey population is divided into two subclasses: (i) prey x in the refuge area and (ii) prey y in the predatory area. We have taken the migration of the prey population from refuge area to predatory area. Also, we have considered a benefit from the antipredation response of the prey population y in presence of cost of fear. Feasible equilibrium points of the proposed system are derived, and the dynamical behavior of the system around equilibria is investigated. Birth rate of prey in predatory region has been regarded as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the interior equilibrium point. Moreover, the conditions for occurrence of transcritical bifurcations have been determined. Further, we have incorporated discrete-type gestational delay on the system to make it more realistic. The dynamical behavior of the delayed system is analyzed. Finally, some numerical simulations are given to verify the analytical results.

Keywords: antipredation response; fear effect; global stability; local bifurcations; prey refuge; time delay
Corresponding author: Guruprasad Samanta, Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah711103, India, E-mail:

Acknowledgments

The authors are grateful to the learned reviewers and the Editor for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare that they have no conflict of interest regarding this article.

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Received: 2020-07-21
Accepted: 2020-08-19
Published Online: 2020-09-28
Published in Print: 2021-01-27

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2020-0195
Keywords for this article
antipredation response; fear effect; global stability; local bifurcations; prey refuge; time delay

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Chemical Physics
  3. Energy levels and transition probabilities of N+, F3+, and Ne4+ ions
  4. Dynamical Systems & Nonlinear Phenomena
  5. Genetic algorithm (GA)–based delay feedback control of chaotic behavior in the voltage mode controlled direct current (DC) drive system
  6. Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge
  7. Gravitation & Cosmology
  8. Cosmology of Tsallis holographic scalar field models in Chern–Simons modified gravity and optimization of model parameters through χ2 minimization
  9. Solid State Physics & Materials Science
  10. Thermal conversion of CBD grown ZnS thin films to ZnO
  11. Studies on birefringence, order parameter and image analysis of liquid crystalline p-n butyloxy/butyl benzoic acid with dispersed ZnO nanoparticles
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