The Lyapunov function plays an important role in the stability theory of dynamical systems. Its counterpart for discrete systems is not studied so much, though importance such increasing. In this letter, attempt made to construct a analog competitive Lotka-Volterra equation. For purpose, logarithmic defined and its effectiveness shown.

The noise-induced pattern formation in a population dynamical model of three interacting species in the coexistence regime is investigated. A coupled map lattice of Lotka-Volterra equations in the presence of multi-plicative noise is used to analyze the spatiotemporal evolution. The spatial correlation of the species concentration as a function of time and of the noise intensity is investigated...

The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...

The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1 n 1 x1 n exp{b1 n −a1 n x1 n −c2 n ∑n s −∞ K2 n−s x2 s }, x2 n 1 x2 n exp{−b2 n − a2 n x2 n c1 n ∑n s −∞ K1 n − s x1 s } and a competitive system xi n 1 xi n exp{bi n − aiixi n − ∑l j 1,j / i ∑n s −∞ Kij n...

In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.

This paper is concerned with the following two-species LotkaVolterra competition-diffusion system in the three-dimensional spatial space { ∂ ∂t u1(x, t) = ∆u1(x, t) + u1(x, t) [1− u1(x, t)− k1u2(x, t)] , ∂ ∂t u2(x, t) = d∆u2(x, t) + ru2(x, t) [1− u2(x, t)− k2u1(x, t)] , where x ∈ R3 and t > 0. For the bistable case, namely k1, k2 > 1, it is well known that the system admits a one-dimensional mo...

In this paper, we consider an anti-periodic Boundary Value Problem for Volterra integro-differential equation of fractional order 1 < α ≤ 2, with generalized Mittag-Leffler function in the kernel. Some existence and uniqueness results are obtained by using some well known fixed point theorems. We give some examples to exhibit our results. c ©2016 All rights reserved.

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

We provide a sufficient condition for the bounded law of iterated logarithms strictly stationary random fields expressable as functional i.i.d. when summation is done on rectangles. The study via control moments an appropriated maximal function. Applications to functionals linear fields, functions Gaussian field and Volterra process are given.

This paper presents a lattice structure for adaptive Volterra systems. The stucture is applicable to arbitrary planes of support of the Volterra kernels. A fast least squares lattice and a fast QR-lattice adaptive nonlinear filtering algorithms based on the lattice structure are also presented. These algorithms share the fast convergence property of fast least squares transversal Volterra filte...