Dynamics of a delayed Lotka-Volterra model with two predators competing for one prey

<p style='text-indent:20px;'>In this paper, we study the local dynamics of a class of 3-dimensional Lotka-Volterra systems with a discrete delay. This system describes two predators competing for one prey. Firstly, linear stability and Hopf bifurcation are investigated. Then some regions of attraction for the positive steady state are obtained by means of Liapunov functional in a restricted region. Finally, sufficient and necessary conditions for the principle of competitive exclusion are obtained.</p>

Existence and Exponential Stability of the Unique Almost Periodic Positive Solution for Discrete Nicholson’s Blowflies Model

This paper deals with a discrete Nicholson’s blowflies model. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by Liapunov functional. We obtain new results and complement the previously obtained results in the past literatures.

Kernel-resolvent relations for an integral equation

We consider a scalar integral equation where |G(t,z)| ≤ ϕ(t)|z|, C is convex, and . Related to this is the linear equation and the resolvent equation . A Liapunov functional is constructed which gives qualitative results about all three equations. We have two goals. First, we are interested in conditions under which properties of C are transferred into properties of the resolvent R which is used in the variation-of-parameters formula. We establish conditions on C and functions b so that as t→∞ and is in L2[0, ∞] implies that as t→∞ and is in L2[0, ∞]. Such results are fundamental in proving that the solution z satisfies z(t) →a(t) as t→∞ and that . This is in final form and no other version will be submitted.

A Result in Artificial Intelligence

Consider a class of artificial intelligence model with finite time–delay. We construct a Liapunov functional. A global stability result is given by means of the analysis and computing method.

On the Global Stability Problem of Multimedia Systems

A global stability analysis for multimedia systems is given by means of the method of Liapunov functional.

Global Stability Analysis of Multimedia Systems

A result of global stability for multimedia systems is given by means of the Liapunov functional method.