Exploring unique dynamics in a predator-prey model with generalist predator and group defense in prey

In the current paper, 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 defense via a generalized response. We show that the model could exhibit finite-time blow-up, contrary to the current literature [Patra et al., Eur. Phys. J. Plus 137(1), 28 (2022)]. We also propose a new concept via which the predator population blows up in finite time, while the prey population quenches in finite time; that is, the time derivative of the solution to the prey equation will grow to infinitely large values in certain norms, at a finite time, while the solution itself remains bounded. 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. The group defense exponent p is seen to significantly affect the basin of attraction. Last, we posit a delayed version of the model with globally existing solutions for any initial data. Both the ordinary differential equation model and the spatially explicit partial differential equation models are explored.