In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

Abstract We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear Lax representation such systems. This method, amounts to reconstruction operator from moments its Weyl function, can be used solving initial-boundary value both It is shown that Miura easily described these moments. Usi...

In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form _ x 1⁄4 xð2 a20x a11xy a02yÞ; _ y 1⁄4 yð 3þ b20x þ b11xyþ b02yÞ; ð1Þ which fulfillment yields the existence in a neighborhood of the origin of a first integral of the form /ðx; yÞ 1⁄4 x3y2 þ h:o:t:, in which case the origin is termed a 2 : 3 resonant center. This system was studied in [13], where...

The adaptive Volterra filter has been successfully applied in nonlinear acoustic echo cancellation (AEC) systems and nonlinear line echo cancellation systems, but its applications are limited by its required computational complexity and slow convergence rate, especially for systems with long memory length. In this paper, we first apply a more general nonlinear filter, the function expansion non...

We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynam...

Lotka-Volterra population biology models are important models that describe the interaction between various biological species considered as predator-prey system. This work describes a Lotka-Volterra population biology model with negative feedback. We show that for this biological model, the predator and prey species have stable coexistence. Then we shall propose ecological monitoring of the po...

The performance of linear acoustic echo cancelers degrades if nonnegligible nonlinear distortion is introduced into the echo path as, e.g., caused by low-cost loudspeaker systems driven at high volume. Adaptive second-order Volterra filters are known to effectively model nonlinear acoustic echo paths. In this contribution we propose an extension of the proportionate NLMS (PNLMS) to second-order...

We show that the flow generated by the totally competitive planar Lotka–Volterra equations deforms the line connecting the two axial equilibria into convex or concave curves, and that these curves remain convex or concave for all subsequent time. We apply the observation to provide an alternative proof to that given by Tineo in 2001 that the carrying simplex, the globally attracting invariant m...

Some scientists are interesting to study in area of harvested ecological modelling. The harvested population dynamics is more realistic than other ecological models. In the present paper, some of the Lotka-Volterra predator-prey models have been considered. In the said models, existing species are harvested by constant or variable growth rates. The behavior of their solutions has been analyzed ...

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...