Article history: Received 19 April 2011 Available online 4 November 2011 Submitted by W. Sarlet

in this paper, an n-species delayed Lotka-Volterra system without delayed intraspecific competitions is considered. It is proved that the system is globally stable for all off-diagonal delays τij ≥ 0 if and only if the interaction matrix A of the system satisfies Condition (WDD).

In this paper, we investigate a delayed predator-prey system with Holling IV functional responses and harvesting terms on time scales. By using coincidence degree theory, we establish the existence of at least two positive periodic solutions for the above model.

We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the Lagrangian framework by treating the action as a Volterra series. It is then possible to derive two equations of motion, one of these is an advanced equation and ...

It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations SVIEs . In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we extend Itô’s formula to a more general form applicable to some kinds of SVIEs. Furthermore, the stabili...

In this article, the homotopy perturbation method is proposed to solve systems of Volterra integral equations of the first kind. Theoretical proposes are presented briefly, so that this paper can be read independently. To illustrate the method some examples are presented. The results reveal that the homotopy perturbation method is very effective and simple and gives the exact solutions.

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, ...

as a model for the competition of n biological species. In this model, xj represents the number of individuals of species j (so Volterra assumes xj > 0), the ajk’s are the interaction coefficients, the εj ’s and the βj’s(> 0) are parameters that depend on the environment. For example, εj > 0 means that species j is able to increase with food from the environment, while εj < 0 means that it cann...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.