The Volterra series model, though a popular tool in modeling many practical nonlinear systems, suffers from the problem of over-parameterization, as too many coefficients need to be identified, requiring very long data records. On the other hand, often it is observed that of all the model coefficients, only a few are prominent while the others are relatively insignificant. The sparsity inherent...

The functional form representation of input-output relationship through Volterra series provides a structured mathematical platform for the study of nonlinear systems. It employs multi-dimensional kernels, which upon convolution with the applied excitation forces, express system response in the form of a power series. Frequency domain transforms of these multi-dimensional kernels provide higher...

This paper aims at introducing nonlinear interactions in the sound synthesis of resonators. Sound is performed using formalism Volterra series which used to describe and simulate weakly models their kernels. Interactions are constraints imposed considered excite (e.g. bowing a string or striking plate) connect resonators together (such as connecting bridge). requires resolve an inverse problem ...

The features of the application of mathematical modeling of nonlinear dynamic systems such as “input-output”, which operate under the conditions of concentrating production, on the basis of finite sums of Volterra integral power series are considered.

The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...