This paper introduces a spatially heterogeneous diffusive predator–prey model unifying the classical Lotka–Volterra and Holling–Tanner ones through prey saturation coefficient, \begin{document}$ m(x) $\end{document} , which is heterogenous it allowed to 'degenerate'. Thus, in some patches of territory species can interact according kinetics, while others effects play significant role on dynamic...

In this paper, a non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps is studied. Firstly, we show that this model has a unique global positive solution under certain conditions. Then, we discuss the sufficient conditions for stochastically ultimate boundedness and obtain the asymptotic behavior of the solution. Finally, sufficient criteria for extinction of all prey and predat...

This paper describes an individual-based model for simulating the swarming behavior of prey in the presence of predators. Predators and prey are represented as agents that interact through radial force laws. The prey form swarms through attractive and repulsive forces. The predators interact with the prey through an anti-newtonian force, which is a nonconservative force that acts in the same di...

BACKGROUND Most ecological models assume that predator and prey populations interact solely through consumption: predators reduce prey densities by killing and consuming individual prey. However, predators can also reduce prey densities by forcing prey to adopt costly defensive strategies. METHODOLOGY/PRINCIPAL FINDINGS We build on a simple Lotka-Volterra predator-prey model to provide a heur...

A class of three-dimensional Gause-type predator-prey model is considered. Firstly, local stability of equilibrium indicating the extinction of top-predator is obtained. Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator-prey system 2005 , to give the global stability of the equilibrium. Secondly, we analyze the stability...

Through natural as well as anthropogenic processes, prey can lose historically important predators and gain novel ones. Both predator gain and loss frequently have deleterious consequences. While numerous hypotheses explain the response of individuals to novel and familiar predators, we lack a unifying conceptual model that predicts the fate of prey following the introduction of a novel or a fa...

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gr...