It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to arbitrary finite dimension. That is, for the «-species autonomous competitive Lotka-Volte...

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...

It is a well known fact that the local stability of an equilibrium point in a system of ordinary differential equations doesnot necessarily imply its global stability. However, the usual methods used in the analysis of stability of equilibrium points in population models establishes only local stability. The restriction to sufficiently small perturbations of the initial conditions frequently ru...

It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) mo...

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 positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feas...

P systems are used to compute predator-prey dynamics expressed in the traditional formulation by Lotka and Volterra. By governing the action of the transition rules in such systems using the regulatory features of the metabolic algorithm we come up with simulations of the Lotka-Volterra equations, whose robustness is comparable to that obtained using Runge-Kutta schemes and Gillespie's Stochast...

Multi-species Lotka±Volterra models exhibit greater instability with an increase in diversity and/or connectance. These model systems, however, lack the likely behavior that a predator will prey more heavily on some species if other prey species decline in relative abundance. We ®nd that stability does not depend on diversity and/or connectance in multi-species Lotka±Volterra models with this `...

The model for the cumulative n citation distribution, as developed in [L. Egghe and I.K. Ravichandra Rao. Theory of first-citation distributions and applications. Mathematical and Computer Modelling 34, 81-90, 2001] is extended to the general source-item situation. This yields a time-dependent Lotka function based on a given (static) Lotka function (considered to be valid for time ). Based on t...

Existence of traveling wave front solutions is established for diffusive and cooperative Lotka–Volterra system with delays. The result is an extension of an existing result for delayed logistic scaler equation to systems, and is somewhat parallel to the existing result for diffusive and competitive Lotka–Volterra systems without delay. The approach used in this paper is the upper–lower solution...

We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction between oscillatory and non-oscillatory regi...