We consider locally defined operators of the form D ◦K where D is the operator of differentiation and K maps the space of continuous functions into the space of n-times differentiable functions. As a corollary we obtain a characterization of the Volterra operator. Locally defined operators acting in the space of analytic functions are also discussed.

Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a “master equation” possessing a bicomplex formulation.

The Lotka – Volterra equation for three species are integrated in an original way obtaining the existence of cycle. No studies of the cycle stability are held. These would be very interesting kind as in two species. However our results are of value.

In this paper, a model composed of two Lotka-Volterra patches is considered. The system consists of two competing species X, Y and only species Y can diffuse between patches. It is proved that the system has at most two positive equilibria and then that permanence implies global stability. Furthermore, to answer the question whether the refuge is effective to protect Y , the properties of posit...

We consider the following system of Volterra intergral equations

f : N × R → R, K : N × N → R, K(n, i) = 0 for n < i, and b : N → R. We regard N× R as a metric subspace of the Euclidean plane R2. By a solution of (E) we mean a sequence x : N→ R satisfying (E) for all large n. We say that x is a full solution of (E) if (E) is satisfied for all n. Moreover, if p ∈ N and (E) is satisfied for all n ≥ p, then we say that x is a p-solution. For the sake of conveni...

Article history: Received 30 September 2008 Received in revised form 18 December 2008 Accepted 8 January 2009 Available online xxxx PACS: 87.23.Cc 87.10.Hk 05.70.Ln

The objective of this paper is to systematically study the qualitative properties of a predator-prey system with two delays. First, we investigate the effect of two distinct delays on stability of the unique positive equilibrium by analyzing the corresponding characteristic equation. The stability criteria involving the delays and the parameters are given. Second, we prove a permanence result f...