Stage structured prey-predator model incorporating mortal peril consequential to inefficiency and habitat complexity in juvenile hunting

Abstract

Dynamic exploration for a predator-prey biosystem of two species with ratio-dependent functional response together with the capability for predation by both juvenile and adult stage of the predator is carried out; coupled with incentive from all the natural documentation acquainting habitat complexity as an armour for the prey and also as a factor effectuating mortality of only the juvenile predators, attributable to their inefficiency. So as to avoid extinction of either of the species and to preserve the food chain of the ecological system, the results pertaining to the existence and stability of all the equilibrium points of the biosystem along with permanence, transcritical and Hopf bifurcation have been thoroughly studied. Excessive predation by juveniles exhibits destabilization of the biosystem through supercritical Hopf bifurcation; likewise, minimal inefficiency of juveniles and habitat complexity spawns extinction and fluctuation of each species, contrarily an abundance of them decimates the predator species. The obtained results and the dependence of the biosystem on some vital parameters are corroborated from a biological viewpoint, through numerical simulation, for implementation of the system in real-life scenario. Interestingly, an illustration reveals an intriguing limit cycle between the proposed system's trivial and axial equilibriums of the proposed system along with the co-existing periodic point for specific parametric values of inefficiency of juvenile predators.

Keywords

• Stability
• Hopf bifurcation
• Limit cycle
• Population dynamics