Besides being structurally unstable, the Lotka-Volterra predator-prey model has another shortcoming due to the invalidity of the principle of mass action when the populations are very small. This leads to extremely large populations recovering from unrealistically small ones. The effects of linear modifications to structurally unstable continuous-time predator-prey models in a (small) neighbour...

This work introduces a new approach for modelling sea surface current from AVISO/Altimeter satellite data. This is based on utilizing of the Volterra series expansion in order to transform the time series of Merged Sea Level Anomaly satellite altimetry data into a real ocean surface current. The basic equation of hydrodynamic has been solved by first order Volterra model. Then, the Volterra ker...

The Lotka-Volterra equations can be used to model the behavior of complex systems in nature. Trajectories in a stable heteroclinic channel describe transient dynamics according to the winnerless competition principle in such a system. The existence of such a channel is guaranteed if the parameters of the Lotka-Volterra equations satisfy a number of conditions. We study under what conditions a h...

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of almost periodic solution in a harvesting Lotka-Volterra recurrent neural networks on time scales. To a certain extent, our work in this paper corrects the defect in [Y.G. Liu, B.B. Liu, S.H. Ling, The almost periodic solution of Lotka-Volterra ...

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simpl...

In this work we introduce the notion of fuzzy volterra dierence equations and study the dynamicalproperties of some classes of this type of equations. We prove some comparison theorems for theseequations in terms of ordinary volterra dierence equations. Using these results the stability of thefuzzy nonlinear volterra dierence equations is investigated.

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In addition, it is described its extreme points. Besides, we study certain limit behaviors of such operators and give some more examples of Volterra operators ...

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

This paper presents an original approach for nonlinear Volterra and NARMAX filter identification. We propose here to use a non persistent excitation of input sequence to excite few terms of the Volterra and NARMAX filter, which must satisfy a set of physical constraints. Expressions have been developped to evaluate the accurate number of excited terms of the Volterra and NARMAX filter.

• TOP OF ARTICLE • INPUT-OUTPUT SYSTEM REPRESENTATION • NONLINEAR DIFFERENTIAL ALGEBRAIC REPRESENTATION • VOLTERRA REPRESENTATION • STATE-SPACE REPRESENTATION • BILINEAR REPRESENTATION • NARMA REPRESENTATION • FUZZY-LOGIC NONLINEAR REPRESENTATION • NONLINEAR REPRESENTATION USING NEURAL NETWORKS • MODEL-FREE REPRESENTATION • FEATURES OF NONLINEAR REPRESENTATIONS • EXAMPLE • CONCLUDING REMARKS • ...