The paper gives necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a ddimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used.

(2) x∆(t) = G(t, x(s); 0 ≤ s ≤ t) := G(t, x(·)) on a time scale T that is unbounded above with 0 ∈ T, where x ∈ R andG : [0,∞)T× R 7→ R is a is rd-continuous function in t and x with G(t, 0) = 0. Throughout this paper, for each continuous function φ : [0, t0]T 7→ R there exists at least one continuous function x(t) = x(t, t0, φ) on an interval [t0, a]T such that it satisfies (2) for t ∈ [t0, a]...

Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as space-dependent, so-called Fokker-Planck diffusion. The invader’s diffusion is taken as neutral Fickian. Furthermore, it is studied how multiplicative environmental noise ...

The asymptotic behavior of a stage-structured predator-prey system is studied using the theory of finite dimensional competitive systems. Using natural conditions on the persistency constant for prey and on the reproduction rate of the mature predators, it is found that the system under consideration has a unique positive equilibrium, which is globally asymptotically stable. Some considerations...

In this paper, we deal with a predator-prey model with diffusion in a heterogeneous environment, and we study the uniqueness and stability of positive steady states as the diffusion coefficient of the predator is small enough.

This paper is a review on some recent works on the Liouville integrability of a large class of Lotka-Volterra systems.

Article history: Received 27 August 2014 Available online 20 January 2015 Submitted by J.J. Nieto