Sound production in musical instruments is the consequence of interactions and wave propagation that include nonlinear phenomena. Simulating these phenomena will enable sound synthesis softwares (such as Modalys, developed at IRCAM) to produce more realistic sounds. In order to do so, nonlinear physical models will be implemented in Modalys software using Green-Volterra kernels. Green-Volterra ...

We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator–prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka–Volterra model. Two levels of meanfield approximations are set up. The simple approximation is equivalent to an extended patch m...

We study a cyclic Lotka-Volterra model of N interacting species populating a d-dimensional lattice. In the realm of a Kirkwood approximation, a critical number of species Nc(d) above which the system fixates is determined analytically. We find Nc = 5, 14, 23 in dimensions d = 1, 2, 3, in remarkably good agreement with simulation results in two dimensions. A cyclic variant of the Lotka-Volterra ...

In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra-Levin equations are given. Our results imply that under the appropriate linear periodic impulsive perturbations, the impulsive stochastic Volterr...

The paper studies the finite-time blow-up theory for a class of nonlinear Volterra integro-differential equations. The conditions for the occurrence of finite-time blow-up for nonlinear Volterra integro-differential equations are provided. Moreover, the finite-time blow-up theory for nonlinear partial Volterra integro-differential equations with general kernels is also established using the blo...

We present a framework to apply Volterra series to analyze multilayered perceptrons trained to estimate the posterior probabilities of phonemes in automatic speech recognition. The identified Volterra kernels reveal the spectro-temporal patterns that are learned by the trained system for each phoneme. To demonstrate the applicability of Volterra series, we analyze a multilayered perceptron trai...

The classical Monad model for bacterial growth in a chemostnt, based on u Michaelis-Menten kinetic analog, is restated in terms of an approximate LotkaVolterra formulation. The parameters of these two formulations are explicitly related; the new model is easier to work with, but yields the same results as the original. The model is then extended to the case where multiple alternate substrates m...

Volterra series have been in the engineering literature for some time now, and yet there have been few attempts to measure Volterra kernels. This paper discusses techniques for measuring the Volterra kernels of weakly nonlinear systems. We introduce a new quick method for measuring the second Volterra kernel which is analogous to pseudo-noise testing of a linear device. To illustrate the discus...

We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the Bäcklund transformations (BT) which are not the ordinary ones. We call them “fractional ” BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (di...

In this paper, the Kalman-Bucy filter is designed for an Ito-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solv...