Stochastic analysis of a prey–predator model with herd behaviour of prey

In nature, a number of populations live in groups. As a result when predators attack such a population the interaction occur only at the outer surface of the herd. Again, every model in biology, being concerned with a subsystem of the real world, should include the effect of random fluctuating environment. In this paper, we study a prey–predator model in deterministic and stochastic environment. The social activity of the prey population has been incorporated by using the square root of prey density in the functional response. A brief analysis of the deterministic model including the stability of equilibrium points is presented. In random environment, the birth rate of prey species and death rate of predator species are perturbed by Gaussian white noises. We have used the method of statistical linearization to study the stability and non-equilibrium fluctuation of the populations in stochastic model. Numerical computations carried out to illustrate the analytical findings. The biological implications of analytical and numerical findings are discussed critically

A Modified Holling-Tanner Model in Stochastic Environment

Recently, a modified version of the so called Holling-Tannermodel isintroduced in the ecological literature. A detailed account of the deterministic dynamicsof this model is presented. The growth rates of the prey and predator are then perturbedby Gaussian white noises to take into account the effect of fluctuating environment. Theresulting stochastic model is cultured by the technique of statistical linearization andcriteria for non-equilibrium fluctuation and stability arederived. Numerical simulationsare carried out. The implications of our analytical findingsare addressed critically

Crowding effects and depletion mechanisms for population regulation in prey-predator intraspecific competition model

The current investigation centres on the consequences of intra-specific rivalry involving predators in the predator-prey equation. A careful account of the investigation is offered mathematically of the model to offer insights into important outcomes that result from the interplay of deterministic and stochastic process. In particular, the steadiness and bifurcation investigation of this model find mention. Allowance is also made in this model for a stochastic environment impacted by white noise. While for this particular version, the global stability is predicated under conditions bordering on stochasticity close to environmental concerns. Rivalry among the predator population is without a doubt accommodating for a various predator-prey models by keeping population stable at a positive interior equilibrium. Numerical solutions obtained for the models support the assumptions governing the study