We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text]...

Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point over the whole parameter space of the system. Discretization effects break the parameter space into several phases where the system exhibits a distinct behavior: The fixed-point becomes ei...

In this paper, input-to-state stability and stabilization conditions in time-delay generalized Persidskii systems are studied. These formulated terms of linear matrix inequalities, which may depend on delay values, be local or global state space. Numerical examples opinion dynamics the Lotka-Volterra model illustrate efficiency proposed results.

In this paper we present a new approach for linear Volterra integral equations that is based on optimal control theory. Some optimal control problems corresponding Volterra integral equation be introduced which we solve these problems by discretization methods and linear programming approaches. Finally, some examples are given to show the efficiency of approach. Index Terms —Volterra integral e...

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, ...

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon ch...

We study S-asymptotically ω-periodic mild solutions of the semilinear Volterra equation u′(t) = (a ∗ Au)(t) + f(t, u(t)), considered in a Banach space X, where A is the generator of an (exponentially) stable resolvent family. In particular, we extend recent results for semilinear fractional integro-differential equations considered in [4] and for semilinear Cauchy problems of first order given ...

The occurrence of chaos in basic Lotka-Volterra models of four competing species is studied. A brute-force numerical search conditioned on the largest Lyapunov exponent indicates that chaos occurs in a narrow region of parameter space but is robust to perturbations. The dynamics of the attractor are studied using symbolic dynamics, and the question of self-organized critical behavior (scale-inv...

An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this paper, we propose a novel DPS modeling approach, in which a high-order nonlinear Volterra series is used to separate the time/space variables. With almost no additional computational complexity, the modeling accuracy is improved more t...