In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations are given. Our results imply that under the appropriate linear periodic impulsive perturbations, the impulsive stochastic Volterr...

The paper studies the finite-time blow-up theory for a class of nonlinear Volterra integro-differential equations. The conditions for the occurrence of finite-time blow-up for nonlinear Volterra integro-differential equations are provided. Moreover, the finite-time blow-up theory for nonlinear partial Volterra integro-differential equations with general kernels is also established using the blo...

We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include t...

In this paper we study the global dynamics of 3–dimensional predator prey Lotka–Volterra systems, which describes two predators competing for food or shared one resource. From theoretical analysis on all parameters of this system, we show that if the resource for prey is limited, then there exist some values of parameters such that two predators and one prey coexist and their population are asy...

A new method for measuring the heating rate (defined as the time rate of change of temperature) and estimating heat flux from the heating rate is proposed. The example problem involves analytic heat conduction in a one-dimensional slab, where the measurement location of temperature or heating rate coincides with the location of the estimated heat flux. The new method involves the solution to a ...

We present a framework to apply Volterra series to analyze multilayered perceptrons trained to estimate the posterior probabilities of phonemes in automatic speech recognition. The identified Volterra kernels reveal the spectro-temporal patterns that are learned by the trained system for each phoneme. To demonstrate the applicability of Volterra series, we analyze a multilayered perceptron trai...

Volterra series based model, which is comprised of uniand multi-convolutions in terms of various inputs, could provide an accurate description of nonlinearities while preserving memory effects missed in static transformations. The basic premise of the Volterra theory of nonlinear systems is that any nonlinear system can be modeled as an infinite sum of multidimensional convolution integrals of ...

The Lotka-Volterra equations are a system of equations proposed to provide a simplified model of twospecies predator-prey population dynamics. In this paper, we investigate the problem of adaptive chaos control and synchronization of a generalized Lotka-Volterra system discovered by Samardzija and Greller (1988). The Samardzija-Greller model is a two-predator, one-prey generalization of the Lot...

A broad class of nonlinear systems can be modeled by the Volterra series representation. However, the practical use of such a representation is often limited due to the large number of parameters associated with the Volterra filter structure. This paper is concerned with the problem of identification of third-order Volterra systems. The SVD technique is used to represent the quadratic Volterra ...