This paper introduces parallel-cascade realizations of truncated Volterra systems with arbitrary, but finite order of nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. Such realizations are very modular and therefore well-suited for VLSI implementation. A systematic way of approxima...

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck's ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed rst-kind Volterra equation is seen to be the limit of a sequence of solutions of well...

In this paper, we introduce a novel algorithm for morphing any accelerogram into a spectrum matching one. First, the seed time series is re-expressed as a discrete Volterra series. The first-order Volterra kernel is estimated by a multilevel wavelet decomposition using the stationary wavelet transform. Second, the higher-order Volterra kernels are estimated using a complete multinomial mixing o...

Nonlinear adaptive filtering techniques, based on the Volterra model, are widely used for the nonlinearities identification in many applications. This paper proposes a new implementation of the third order LMS Volterra filter. A third order nonlinear system with memory is identified using the new LMS algorithm implementation for the Volterra kernels estimation. The accuracy of the proposed algo...

Abstract A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear Fredholm, Volterra and Volterra-Fredholm integral equations of first and second kind. The proposed method is an extension of the Haar wavelet method [1–3] from one-dimensional nonlinear integral equations (Fredholm and Volterra) to twodimensional nonlinear integral equations (Fredholm, Volterra and V...

Subharmonic images are becoming interestingly in medical ultrasound, as the improvement of contrastto-tissue ratio (CTR). However, an important part for image enhancement is processing techniques. In this study, frequency response functions (FRFs) of multiple-input-multiple-output (MIMO) Volterra systems were used to investigate potentially possible in separating subharmonic frequency for the q...

Abstract This work is to analyze a nonlocal dispersal model governed by Volterra type integral and two space integrals. A weighted included, an existence result of solutions for this proved. We assume suitably Hartman-type sign condition use sufficiently regular measure noncompactness. Finally, the degree theory referring condensing operators applied.

Abstract In this paper, the representation of the exact solution to the nonlinear Volterra-Fredholm integral equations will be obtained in the reproducing kernel space. The exact solution is represented in the form of series. Its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained. The error of the approximate solution is monotone deceasi...

Global dynamical behaviors of the competitive Lotka-Volterra system even in 3-dimension are not fully understood. The Lyapunov function can provide us such knowledge once it is constructed. In this paper, we construct explicitly the Lyapunov function in three examples of the competitive LotkaVolterra system for the whole state space: (1) the general 2-dimensional case; (2) a 3-dimensional model...

Integrability and linearizability of the Lotka–Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka–Volterra systems. Sufficient conditions for integrable Lotka–Volterra systems with 3 : q resonance are given. In the particular cases of 3 : 5 and 3 : 4 r...