A discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with BeddingtonDeAngelis functional responses is proposed. By using Gaines andMawhin’s continuation theorem of coincidence degree theory, ...

We have investigated wave solutions of the Predator–Prey (PP) model with fractional derivative order by novel three modified mathematical methods help Mathematica platform. The derived are in form distinct functions such as trigonometric, hyperbolic, exponential and rational functional. For physical phenomena model, some plotted 2-dimensional 3-dimensional inserting specific values to attached ...

This investigation examines how a predator-induced reduction in activity of a prey species (a ‘‘nonlethal’’ predator effect) affects the growth rate of the prey and, indirectly, the growth rate of competitors of the prey. We further determine how the magnitudes of these effects depend on density of the prey species. We develop a foraging model that predicts a predator will reduce the growth of ...

A delayed periodic predator–prey model with stage structure for predator is proposed. It is assumed that immature individuals and mature individuals of the predator are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solutions of the mo...

We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is infinitely large, is the Volterra system (with density-dependent prey reproduction) which is well known to fail to predict cycles. This difference in behavior can be trac...

Alarm-calling behaviour is common in many species that suffer from predation. While kin selection or reciprocal altruism are typically invoked to explain such behaviours, several authors have conjectured that some alarm calls may instead be costly signals sent by prey to inform approaching predators that they have been detected. We develop a general game-theoretical model, the watchful babbler ...

Keywords--Prey-predator system, Time delay, Stability, Hopf bifurcation, Periodic solutions. 1. I N T R O D U C T I O N After the seminal models of Volterra and Lotka in the mid-1920s, predator-prey systems with delay have been studied extensively in recent years. There have been many results on stability, oscillation, persistence, and existence of positive periodic solutions, see for example, ...

In this paper we analyse a predator-prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig-MacArthur predator-prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator-...