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

Kalabušić, Senada; Drino, Džana; Pilav, Esmir

doi:10.1007/978-3-031-25225-9_12

Springer Proceedings in Mathematics &Amp; Statistics

2023

DOI: 10.1007/978-3-031-25225-9_12

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

Senada Kalabušić

Džana Drino²,

Esmir Pilav³

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Cited by 2 publications

References 34 publications

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A Generalized Beddington Host–Parasitoid Model with an Arbitrary Parasitism Escape Function

Bešo,

Kalabušić,

Pilav

et al. 2024

Int. J. Bifurcation Chaos

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This research delves into the generalized Beddington host–parasitoid model, which includes an arbitrary parasitism escape function. Our analysis reveals three types of equilibria: extinction, boundary, and interior. Upon examining the parameters, we discover that the first two equilibria can be globally asymptotically stable. The boundary equilibrium undergoes period-doubling bifurcation with a stable two-cycle and a transcritical bifurcation, creating a threshold for parasitoids to invade. Furthermore, we determine the interior equilibrium’s local stability and analytically demonstrate the period-doubling and Neimark–Sacker bifurcations. We also prove the permanence of the system within a specific parameter space. The numerical simulations we conduct reveal a diverse range of dynamics for the system. Our research extends the results in [Kapçak et al., 2013] and applies to a broad class of the generalized Beddington host–parasitoid model.

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A Generalized Beddington Host–Parasitoid Model with an Arbitrary Parasitism Escape Function

Bešo,

Kalabušić,

Pilav

et al. 2024

Int. J. Bifurcation Chaos

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Strong Allee Effect and Evolutionary Dynamics in a Single-Species Ricker Population Model

Mokni¹,

Ch-Chaoui²

2023

J. Biol. Syst.

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In this paper, a discrete-time Ricker population model with the strong Allee effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and asymptotic stability of the unique positive equilibrium are studied. Second, Neimark–Sacker and period-doubling bifurcations of this discrete model were carried out, and corresponding bifurcation conditions were obtained. Third, the pole placement method and the hybrid control strategy have been used to control the chaos produced by these bifurcations. Finally, we use MATLAB software to carry out some numerical simulations to analyze the rich dynamics of the system as well as to verify our theoretical results.

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

Cited by 2 publications

References 34 publications

A Generalized Beddington Host–Parasitoid Model with an Arbitrary Parasitism Escape Function

A Generalized Beddington Host–Parasitoid Model with an Arbitrary Parasitism Escape Function

Strong Allee Effect and Evolutionary Dynamics in a Single-Species Ricker Population Model

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