Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series c...

We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction between oscillatory and non-oscillatory regi...

1. The KM system In two seminal papers [9] for the modern theory of integrable systems Kac and vanMoerbeke introduced the system of o.d.e.’s u̇i = e ui+1 − ei−1 , i = 1, . . . , n, (1) where formally e0 = en+1 = 0. They showed, for example, that this system arises as a finite-dimensional aproximation of the famous KdV equations. Shortly after, Moser [10] showed that this system can be related to...

An ef®cient implementation of the Volterra ®lter is presented which uses a frequency domain representation to reduce the number of computations. The multidimensional convolution of the Volterra ®lter is transformed to the frequency domain giving a transformed input matrix which is sparse and obtained directly from a one-dimensional Fourier transform. In addition to the sparse nature of the tran...

Texture is an important characteristic di erentiating objects or regions of interest in an image. A variety of approaches to texture analysis has previously been proposed; the approach in this paper is from the stochastic eld, whereby a two-dimensional Volterra model is used to represent a texture eld. Statistical moments are introduced as a means of determining the Volterra model generator for...

Abstract: This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three fricti...

In this paper we study the limit cycles bifurcating from a nonisolated zero-Hopf equilibrium of a differential system in R3. The unfolding of the vector fields with a non-isolated zero-Hopf equilibrium is a family with at least three parameters. By using the averaging theory of the second order, explicit conditions are given for the existence of one or two limit cycles bifurcating from such a z...

For three-dimensional competitive Lotka-Volterra systems, Zeeman (1993) identified 33 stable equivalence classes. In this paper we show that: in the case of a heteroclinic cycle on the boundary of the carrying simplex of three-dimensional competitive Lotka-Volterra systems (class 27 in Zeeman’s classification), the conditions (a) there is a pair of purely imaginary eigenvalues at an interior eq...