Permanence for the Michaelis–Menten type discrete three-species ratio-dependent food chain model with delay

Permanence for a Discrete Model with Feedback Control and Delay

The permanence of a single-species population discrete model with feedback control is considered. We found that if we use the method of comparison theorem, then the additional condition, to some extent, is necessary. But for the system itself, this condition may not be necessary. Here, we use new methods instead of the comparison theorem to get the permanence of the system in consideration; the...

Ratio-Dependent Food Chain Models with Three Trophic Levels

In this paper we study a food chain model with three trophic levels and Michaelis-Menten type ratio-dependent functional response. Distinctive feature of this model is the sensitive dependence of the dynamical behavior on the initial populations and parameters of the real world. The stability of the equilibrium points are also investigated. Keywords—Food chain, Ratio dependent models, Three lev...

DYNAMIC COMPLEXITY OF A THREE SPECIES COMPETITIVE FOOD CHAIN MODEL WITH INTER AND INTRA SPECIFIC COMPETITIONS

The present article deals with the inter specific competition and intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predator sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are e...

Bifurcation analysis and control of chaos for a hybrid ratio-dependent three species food chain

A Food Chain Model Holling Type II with Distributed Delay

In this research we introduce and study, analytic and numerically, a model of chemostat with distributed delay. This a generalization of the model, with no delay, first treated by Kuang. We give conditions for asymptotic stability, survival of species or extinction of them. This research has been partially supported by Central Bank of Venezuela. 2050 Mario Cavani et al. Mathenatics Subject Clas...