We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m− 1)-dimensional simplex, where l ∈ {0, 1, ...,m}. The l-Volterra operator is a Volterra operator if and only if l = m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m = 2 and m = 3 we describe behavior of ...

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of ...

Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the syste...

Nonlinear intersymbol interferences (ISI) often arise in voiceThe major drawback of the Volterra approach is the enormous band communication channels at high transmission rates or in complexity. Even when the symmetry in the 3rd order Volterra satellite channels due to nonlinearities in the power amplifiers. Proposed equalizers for the cancellation of these nonlinear interferences are mainly ba...

We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka–Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka–Volterra model ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t − τ)] into the Itô form dx(t)= dia...

In this paper we stochastically perturb the delay Lotka–Volterra model ẋ(t)= diag(x1(t), . . . , xn(t))[A(x(t)− x̄)+B(x(t − τ )− x̄)] into the stochastic delay differential equation (SDDE) dx(t)= diag(x1(t), . . . , xn(t)){[A(x(t)− x̄)+B(x(t − τ )− x̄)]dt + σ (x(t)− x̄)dw(t)}. The main aim is to reveal the effects of environmental noise on the delay Lotka–Volterra model. Our results can essentially ...

The present work addresses the identification of third-order Volterra models from input-output process data. Building on previous studies regarding input sequence design for third-order Volterra models (Soni and Parker, 2004), a new reduced-length sequence is designed to identify third-order sub-diagonal kernels. This input sequence leads to a 30% reduction in the data required to accurately es...

Abstract—We propose an analog integrated circuit that implements a resonate-and-fire neuron (RFN) model based on the Volterra system. The RFN model is a simple spiking neuron model that exhibits dynamic behavior observed in biological neurons, such as fast subthreshold oscillation, post-inhibitory rebound, and frequency preference. The RFN circuit was derived from the Volterra system to mimic s...