1. Exploring unique dynamics in a predator-prey model with generalist predator and group defence in prey
- Author
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Srivastava, Vaibhava, Antwi-Fordjour, Kwadwo, and Parshad, Rana D.
- Subjects
Mathematics - Analysis of PDEs ,FOS: Biological sciences ,Populations and Evolution (q-bio.PE) ,FOS: Mathematics ,Dynamical Systems (math.DS) ,Mathematics - Dynamical Systems ,Quantitative Biology - Populations and Evolution ,Analysis of PDEs (math.AP) - Abstract
In the current manuscript, we consider a predator-prey model where the predator is modeled as a generalist using a modified Leslie-Gower scheme, and the prey exhibits group defence via a generalised response. We show that the model could exhibit finite time blow-up, contrary to the current literature (Eur. Phys. J. Plus 137, 28). We also propose a new concept via which the predator population blows up in finite time while the prey population quenches in finite time. The blow-up and quenching times are proved to be one and the same. Our analysis is complemented by numerical findings. This includes a numerical description of the basin of attraction for large data blow-up solutions, as well as several rich bifurcations leading to multiple limit cycles, both in co-dimension one and two. Lastly, we posit a delayed version of the model with globally existing solutions for any initial data.
- Published
- 2023