In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero curvature representation, negative Volterra flows are proposed. We also propose the mixed Volterra flows, which come from positive and negative volterra flows. F...

Discrete-time Volterra models play an important role in many application areas. The main drawback of these models is their parametric complexity due to the huge number of their parameters, the kernel coefficients. Using the symmetry property of the Volterra kernels, these ones can be viewed as symmetric tensors. In this paper, we apply tensor decompositions (PARAFAC and HOSVD) for reducing the ...

In the present paper we introduce a notion of homotopy of two Volterra operators which is related to fixed points of such operators. It is establish a criterion when two Volterra operators are homotopic, as a consequence we obtain that the corresponding tournaments of that operators are the same. This, due to [4], gives us a possibility to know some information about the trajectory of homotopic...

In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well Weyl type functions. We also several important subclasses of the class reconsider notion semi-$c$-periodicity in setting, working general framework Lebesgue spaces with variable exponent. provide certain applications our results to abstract Volterra integro-d...

Nonlinear adaptive filtering techniques are widely used for the nonlinearities identification in manny applications. This paper investigates the performances of the Volterra estimator by considering a nonlinear system identification application. The Volterra estimator parameters are compared with those of a linear estimator. For the nonlinear estimator, based on a second order RLS Volterra filt...

A great many of processes in a nature are nonlinear, so their modeling requires an embedding of nonlinear parts into the model structure. One of the popular approaches to the nonlinear system modeling are Volterra series. Unfortunately, already the second order Volterra kernel requires high amount of coefficients for its identification and therefore a large number of computations for its realiz...

This study proposes a generalized grey Lotka–Volterra model with finite number of variables. The is obtained by applying the modelling method to estimate parameters dimensional quadratic system. Subsequently, used analyze competition and cooperation relationship between four macroeconomic indicators, namely Gross Domestic Product, Export, Import Investment, obtain short-time forecasting for the...

In this paper we first prove the equivalence between the system of coupled Volterra gyrostats and a special class of energy-conserving low-order models. We then extend the definition of the classical Volterra gyrostat to include nonlinear feedback, resulting in a class of generalized Volterra gyrostats. Using this new class of gyrostats as a basic building block, we present an algorithm for con...

| This paper studies approximations for a class of nonlinear lters known as Volterra lters. Although the Volterra lter provides a relatively simple and general representation for nonlinear ltering, often it is highly over-parameterized. Due to the large number of parameters, the utility of the Volterra lter is limited. The over-parameterization problem is addressed in this paper using a tensor ...

This paper presents performance analysis of an adaptive Volterra/Hybrid equalizer in a nonlinear magneto-optic data storage channel. In a data storage system, nonlinear intersymbol interference (ISI) is one of the limiting factors for high storage density. Volterra and Hybrid (combination of linear and Volterra) equalizers are proposed and developed for compensation of nonlinear ISI. The use of...