Chaos control via feeding switching in an omnivory system.

Tanabe and Namba (Ecology, 86, 3411-3414) studied a three species Lotka-Volterra model with omnivory and explored that omnivory can create chaos. It is well documented that predator switching is a similar biological phenomenon to omnivory and likely to occur simultaneously. In the present paper, the tri-trophic Lotka-Volterra food web model with omnivory and predator switching is re-investigated. We observe that if we incorporate predator switching in the system and the intensity of predator switching increases above a threshold value, then the system will be stable from chaotic dynamics. To study the global dynamics of the system extensive numerical simulations are performed. Our analytical and numerical results suggest that predator switching mechanism enhances the stability and the persistence of a food chain system.

Analysis of a predator-prey system with predator switching.

In this paper, we consider an interaction of prey and predator species where prey species have the ability of group defence. Thresholds, equilibria and stabilities are determined for the system of ordinary differential equations. Taking carrying capacity as a bifurcation parameter, it is shown that a Hopf bifurcation can occur implying that if the carrying capacity is made sufficiently large by enrichment of the environment, the model predicts the eventual extinction of the predator providing strong support for the so-called 'paradox of enrichment'.

A study of prey-predator relations for mammals.

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.

The stability of internal equilibria in predator-prey models with breeding suppression.

We present two models that represent the suppression of breeding by prey in response to short-term increases in predation pressure. For both of these models, we have been able to produce analytic conditions for the local stability of the interior steady state, in terms of the values of combinations of these parameters. Although our models are as simple as possible to capture the effect of breeding suppression, the expressions for local stability, even in their simplest form, are complex. Thus, we come to the important conclusion that there is no simple and general rule for the effect of the behaviours described here (anti-predatory breeding suppression and prey switching by predators) on the stability of population dynamics. Rather, effects will be system specific. However, we hope that the results and methodological framework outlined here will provide a useful tool for others to investigate the consequences for particular real systems.