In this article, we study a ratiodependent predator-prey system where predator population is subjected to harvesting with MichaelisMenten type harvesting rate. We study the existence of heteroclinic bifurcations in an exploited predatorprey system by using Melnikov’s method. Our simulation results also show that the system may exhibit monostability, bistability and tristability depending on the...

Paradoxically, enrichment can destabilize a predator-prey food web. While adaptive dynamics can greatly influence the stability of interaction systems, few theoretical studies have examined the effect of the adaptive dynamics of interaction-related traits on the possibility of resolution of the paradox of enrichment. We consider the evolution of attack and defence traits of a predator and two p...

We study a tritrophic food chain model which is based on Schnakenberg type kinetics. This model is realistic in a predator-prey context if cooperation of predators is prevalent in the system. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. It is an extension of the Schnakenberg model sugge...

Swarming behaviours in animals have been extensively studied owing to their implications for the evolution of cooperation, social cognition and predator– prey dynamics. An important goal of these studies is discerning which evolutionary pressures favour the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attack...

Swarming behaviours in animals have been extensively studied owing to their implications for the evolution of cooperation, social cognition and predator-prey dynamics. An important goal of these studies is discerning which evolutionary pressures favour the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacki...

The predator-prey-type ecosystem is investigated, taking into account the time-delay effect of the prey population on the predator population, as well as random variations in the birth rate of the prey and the death rate of the predators. The stochastic averaging procedure is applied to obtain the probability distributions of the predator and prey populations at the state of statistical station...

We investigate the influence of asymmetric interactions on coevolutionary dynamics of a predator-prey system by using the theory of adaptive dynamics. We assume that the defense ability of prey and the attack ability of predators all can adaptively evolve, either caused by phenotypic plasticity or by behavioral choice, but there are certain costs in terms of their growth rate or death rate. The...

We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation...

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presum...