2023/06/14 by Vaibhava Srivastava, Srivastava, Vaibhava, Kwadwo Antwi‐Fordjour +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2306.13666
openalex publication_date 2023/06/14 · openalex created_date 2023/06/28 · openalex updated_date 2026/07/28
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.