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...

A class of cross diffusion parabolic systems given on bounded domains of IR, with arbitrary n, is investigated. We show that there is a global attractor with finite Hausdorff dimension which attracts all solutions. The result will be applied to the generalized Shigesada, Kawasaki and Teramoto (SKT) model with Lotka-Volterra reactions. In addition, the persistence property of the SKT model will ...

The dynamic economic behavior in most integrated assessment models linking economic growth to climate change involves a differential equation solved by Jacob Bernoulli in 1695. Using the dynamic integrated climate economy (DICE) model and freezing exogenous variables at initial values, this dynamic is shown to produce implausible projections on a 60-year time frame. If world capital started at ...

In the present paper we study a tri-trophic Lotka-Volterra food web model with omnivory and predator switching. We observe that if the intensity of predator switching increases the chaotic behavior of the omnivory model will be reduced. We conclude that the predator switching mechanism enhances the stability of an otherwise chaotic system.

A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model [1, 2] of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are repre...

The study examines temporal trends in population abundance and distribution of a predator and prey species using a spatial diffusion model. Using Chebyshev Spectral Methods in MATLAB®, we were able to develop a model composed of two partial differential equations to simulate and predict population growth and range expansion for the two species. The foundation of the modeling program is a diffus...

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...