Exploring cooperative hunting dynamics and PRCC analysis: insights from a spatio-temporal mathematical model

Abstract

The proposed mathematical model explores the intricate dynamics of a predator-prey system involving prey infection and cooperative hunting of predators. The model incorporates habitat complexity, emphasizing its influence on ecological interactions. The well-posedness of the system has rigorously been examined in a temporal setting and also conducted stability analysis. The bifurcation analysis reveals the existence of several local bifurcations on the system, namely transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation. Furthermore, these investigations delineate the two-dimensional bifurcations including Bogdanov–Takens and cusp bifurcations for different parametric combinations. With suitable choices of parameter values, the proposed model exhibits diverse dynamic phenomena, including bistable and tri-stable behavior. Latin hypercube sampling is utilized to conduct uncertainty analysis on input parameters, aiming to observe their effects on population dynamics. Subsequently, Kendall’s tau and Spearman’s rank correlation coefficients are also computed to investigate the impact of these uncertainties on the population. In the later part, a spatio-temporal system is proposed with two-dimensional diffusion terms to obtain the conditions for Turing instability. Numerical simulations have been conducted to observe the emergence of spatial patterns and the impact of predator cooperation in these patterns. The study provides valuable insights into the dynamics of complex ecological systems, emphasizing the interplay of spatial and temporal factors in shaping population dynamics and predator-prey interactions.