Recently, some biologists have argued that the ratio-dependent predator-prey model is more appropriate than the Gauss-type models for modelling predator-prey interactions where predation involves searching processes. This is strongly supported by numerous laboratory experiments and observations [1, 2, 3, 4, 10, 11, 12]. Many authors [1, 5, 7, 13, 14] have observed that the ratio-dependent preda...

Spatial heterogeneity (patchiness) in certain predator-prey situations has been observed even though their environment appears homogeneous. As a model mechanism to explain this patchiness phenomenon we propose a predator-prey interaction system with diffusive effects. We show that when the diffusion of the prey is small compared with that of the predator the non-linearity which we call a hump e...

A predator’s per capita feeding rate on prey, or its functional response, provides a foundation for predator–prey theory. Since 1959, Holling’s prey-dependent Type II functional response, a model that is a function of prey abundance only, has served as the basis for a large literature on predator–prey theory. We present statistical evidence from 19 predator–prey systems that three predator-depe...

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...

We study a supply 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 and if there is practically an unlimited pool of prey, i.e. the predators will not feel the impact of the limited amount of prey due to its large quantity. The system also serves as a model for a sequence of irrever...

In this paper, a delayed ratio-dependent Holling-III predator-prey system with stage-structured and impulsive stocking on predator and continuous harvesting on prey is considered. We obtain sufficient conditions of the global attractivity of prey-extinction periodic solution and the permanence of the system. These results show that the behavior of impulsive stocking on predator plays an importa...

The stability of predator-prey system subject to the Allee effect is of considerable interest in recent times. The present investigation is an attempt to observe the stability nature of a discrete-time predator-prey system with Allee effect on predator, prey and on both the population. We have obtained the conditions for which the equilibrium points of each of the three cases are asymptotically...

The objective of this paper is to investigate the effect of prey-taxis on predator–prey models with Paramecium aurelia as the prey and Didinium nasutum as its predator. The logistic Lotka–Volterra predator–prey models with prey-taxis are solved numerically with four different response functions, two initial conditions and one data set. Routh–Hurwitz’s stability conditions are used to obtain the...

We have constructed a synthetic ecosystem consisting of two Escherichia coli populations, which communicate bi-directionally through quorum sensing and regulate each other's gene expression and survival via engineered gene circuits. Our synthetic ecosystem resembles canonical predator-prey systems in terms of logic and dynamics. The predator cells kill the prey by inducing expression of a kille...