Spatiotemporal behavior of a generalist predator-prey system with harvesting phenomena

Of concern, the present article is a theoretical investigation on the reaction-diffusion interacting species model system including prey harvesting and the alternative food source for the predator maintained partially by Beverton-Holt-like food. Major attention is focused on the influence of alternative food source for the predator in the event of prey harvesting on the dynamical complexity of the system. The existence of equilibria together with their topological classification concerning positive coexisting equilibria of the system is thoroughly explored. The threshold of extinction for interacting species, the stability of feasible equilibria, and the persistence scenario as well are examined analytically. The parametric constraint for subcritical Hopf bifurcation emerging from altering harvesting efforts is established through normal form setting. The perception of the local bifurcation structure of codimensions 1 and 2 depending on the model parameters of significance is also explored. Special emphasis is paid on the sensitivity analysis of the model system so as to examine the effect of harvesting and alternative food source for sustaining biomass balance. The existence and stability of nonnegative equilibria together with Turing instability corresponding to spatiotemporal system are, however, not ruled out from the present pursuit. The evolution of diffusion-driven pattern formation with the inclusion of spots, stripes, labyrinthine, stripe-hole mixtures, and hole replication is well-depicted in 2D$$ 2D $$ space influenced by both the harvesting and additional food source of the dynamical system. Extensive numerical simulations are performed in order to establish all the theoretical outcomes in terms of stability of the system and its sustainable development.