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Bifurcation and Stability of a Ricker Host-Parasitoid Model with a Host Constant Refuge and General Escape Function

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Advances in Discrete Dynamical Systems, Difference Equations and Applications (ICDEA 2021)

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Abstract

Motivated by the Ricker model and paper [7], in this paper, we investigate the dynamics of a class of Ricker host-parasitoid models, wherein for each generation, a constant number of hosts are safe from attack by parasitoids, and the Ricker equation governs the host population. For the escape function, we take a general probability function that satisfies specific conditions. We show that the system always possesses exclusion equilibrium. Furthermore, the unique interior equilibrium exists under certain conditions. We show that the exclusion equilibrium undergoes the transcritical and period-doubling bifurcations, while Neimark–Sacker and period-doubling bifurcations occur at the interior equilibrium point. We investigate the boundedness of solutions. We prove the global attractivity result for the interior equilibrium. Finally, we show the uniform persistence of the system, ensuring the long-term survival of both species. Then, using a few well-known escape functions, we provide numerical simulations to confirm our theoretical findings.

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Acknowledgements

The authors thank the anonymous referee for the helpful comments.

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Authors and Affiliations

  1. Department od Mathematics, University of Sarajevo, Zmaja od Bosne 33-35, Sarajevo, Bosnia and Herzegovina

    Senada Kalabušić, Džana Drino & Esmir Pilav

Authors
  1. Senada Kalabušić
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  2. Džana Drino
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  3. Esmir Pilav
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Corresponding author

Correspondence to Senada Kalabušić .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. University of Rhode Island, Kingston, RI, USA

    Mustafa R. S. Kulenović

  3. University of Sarajevo, Sarajevo, Bosnia and Herzegovina

    Senada Kalabušić

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Kalabušić, S., Drino, D., Pilav, E. (2023). Bifurcation and Stability of a Ricker Host-Parasitoid Model with a Host Constant Refuge and General Escape Function. In: Elaydi, S., Kulenović, M.R.S., Kalabušić, S. (eds) Advances in Discrete Dynamical Systems, Difference Equations and Applications. ICDEA 2021. Springer Proceedings in Mathematics & Statistics, vol 416. Springer, Cham. https://doi.org/10.1007/978-3-031-25225-9_12

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