A delay non-autonomous model for the combined effects of fear, prey refuge and additional food for predator

Catastrophic and noncatastrophic population crashes in a bitrophic system with dynamic additional food provision to cooperative predators

In this article we contemplate the dynamics of an additional food-provided prey-predator system. We assume that the behavior of cooperative predators induces fear in prey, which radically affects the prey's birth and death rates. We observe that the structural instability imposed by strong cooperative hunting among predators goes away with higher intensities of fear levels affecting the prey's reproductive output and mortality. High levels of prey refuge are not conducive to the survival of predators. In such a situation, adequate supply of high-quality additional food is favorable regarding the persistence and stability of the system. Interestingly, the system potentially exhibits two stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle-node and backward bifurcations, and associated hysteresis effects with prey refuge along with additional food quantity and quality. In the stochastic environment, the system experiences critical transitions through bifurcation-induced tipping events with time-varying additional food for predators. Enhanced disturbance events promote noise-induced switching and tipping events. Finally, our investigation explores whether impending population crashes resulting from the variability of additional food quantity and quality can reliably be predicted using early warning signals in the context of redshifted noise. Overall, our results may provide insights for finding control strategies in the context of community ecology.

AN ECOEPIDEMIC SEASONALLY FORCED MODEL FOR THE COMBINED EFFECTS OF FEAR, ADDITIONAL FOODS AND SELECTIVE PREDATION

In this paper, we study a predator–prey system in which the prey population is infected from a parasite and the growth of susceptible prey is suppressed due to fear of predation. We consider that the predators have the ability to distinguish between the susceptible and infected prey items, and they avoid the infected ones to reduce fitness cost. The predators are assumed to die naturally and also due to intraspecific competition. The proposed model is analyzed mathematically for the feasibility and stability of the system’s equilibria. We also discuss the existence of Hopf bifurcation by taking the feeding preference of predators as a bifurcation parameter. We perform global sensitivity analysis to identify model parameters having significant impact on the density of predator population in the ecosystem. Our simulation results show the stabilizing role of selective feeding of predators whereas fear factor and disease prevalence induce limit cycle oscillations. Feeding more the predators with additional foods bring stability in the system by evacuating the persistent oscillations. To model the situation more realistically, we consider that the parameters representing the cost of fear and the feeding preference of predators vary with time. For the seasonally forced system, conditions are obtained for which the system has at least one positive periodic solution; global attractivity of the positive periodic solution is also discussed. Our seasonally forced model demonstrates the appearance of a unique periodic solution, higher periodic solutions and complex bursting patterns.