The aim of this work is to study a modified version the four-dimensional Lotka-Volterra model. In model, all four species grow logistically. This model has at most sixteen possible equilibrium points. Five them always exist without any restriction on parameters while existence other points subject fulfillment some necessary and sufficient conditions. Eight are unstable rest locally asymptotical...

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...

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

The following conjecture of M. L. Zeeman is proved. If three interacting species modeled by a competitive Lotka–Volterra system can each resist invasion at carrying capacity, then there can be no coexistence of the species. Indeed, two of the species are driven to extinction. It is also proved that in the other extreme, if none of the species can resist invasion from either of the others, then ...

A 3D competitive Lotka-Volterra equation with two limit cycles is constructed. Keywords-Lotka-Volterra equations, Competitive systems, Limit cycles, Hopf bifurcation. INTRODUCTION It is a classical result (due to Moisseev 1939 and/ or Bautin 1954, see [l, p. 213, Section 12, Example 71 or [2, 18.21) that 2D Lotka-Volterra equations cannot have limit cycles: if there is a periodic orbit, then th...

We introduce a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps solution above given process (lower obstacle). prove existence and uniqueness fixed point argument derive comparison result. Moreover, we show how our problem is related to time-inconsistent optimal stopping an strategy.

Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identificat...