Since Lotka and Volterra’s seminal and pioneering works (see [10]) many decades ago, modeling of interacting, competing species have received considerable attention in the fields of biology, ecology, mathematics (for example, see [3, 9]). In their remarkably simple deterministic model, Lotka and Volterra considered two coupled nonlinear differential equations that mimic the temporal evolution o...

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.

In the paper stochastic Volterra equations of nonscalar type are studied using resolvent approach. The aim of this note is to provide some results on stochastic convolution and integral mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials.

The speech production can be modeled by linear and nonlinear systems. In this contribution a time variable nonlinear Volterra system is used to model the fluctuations of the voiced excitation while a linear system models the resonances of the speech production system. The estimation of the Volterra system is performed by a prediction algorithm. This is enabled by a description of the prediction...

This paper presents a suboptimum custom-tailored (SCT) model for power amplifiers (PAs). Based on the pruned Volterra series, the SCT model is developed by using a recursive optimum-term selecting (ROS) algorithm with an offline characterization process. The proposed model sacrifices accuracy in comparison with the custom-tailored (CT) model derived from the general Volterra series. But the for...

Wavelet packet division multiplexing (WPDM) is a high-capacity, flexible and robust orthogonal multiplexing scheme in which the message signals are waveform coded onto wavelet packet basis functions for transmission. However, WPDM suffers from severe performance degradation in the presence of high-power amplifier (HPA) nonlinearities. In this paper, data predistortion using the pth-order Volter...

The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation and detection based on Volterra filters. Volterra filters have a clear hierarchy of computational complexities and performances, depend onl...

In recent years, non-autonomous delay differential equations have been used in the study of population dynamics, ecology and epidemic. Among those equations, a famous model for population is the Lotka-Volterra competition system. Due to the various seasonal effects present in real life situation, it is reasonable and practical to study the Lotka-Volterra competition system with periodic coeffic...

Truncated Volterra expansions model nonlinear systems encountered with satellite communications, magnetic recording channels, and physiological processes. A general approach for blind deconvolution of single-input multiple-output Volterra finite impulse response (FIR) systems is presented. It is shown that such nonlinear systems can be blindly equalized using only linear FIR filters. The approa...

The robust nonlinear adaptive filtering problem based on Volterra model is researched when the input and output observation data are both corrupted by noise in this paper. On the basis of minimizing Volterra total mean square error (VTMSE), a robust total least mean square adaptive filtering algorithm for nonlinear Volterra filter is proposed. The performance analysis demonstrates that the robu...