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 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...

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 ...

Volterra series have been in the engineering literature for some time now, and yet there have been few attempts to measure Volterra kernels. This paper discusses techniques for measuring the Volterra kernels of weakly nonlinear systems. We introduce a new quick method for measuring the second Volterra kernel which is analogous to pseudo-noise testing of a linear device. To illustrate the discus...

We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the Bäcklund transformations (BT) which are not the ordinary ones. We call them “fractional ” BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (di...

In this paper, the Kalman-Bucy filter is designed for an Ito-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solv...

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

This paper provides new solutions to the nonlinear system identification problem when the input to the system is a stationary non-Gaussian process. We propose the use of a model called the Hammerstein series, which leads to significant reductions in both the computational requirements and the mathematical tractability of the nonlinear system identification problem. We show that unlike the Volte...

Several nonlinear adaptive techniques have been proposed for modelling nonlinear channels with memory. These techniques include Volterra series, wavelet networks, neural networks, etc. See [11, 6] for a review. For example, adaptive Volterra series have been applied in [1] for modelling digital satellite channels. These Volterra models do not characterize each element of the channel. They provi...