We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for th...

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 ...

Chemical reaction networks with generalized mass-action kinetics lead to powerlaw dynamical systems. As a simple example, we consider the Lotka reactions and the resulting planar ODE. We characterize the parameters (positive coefficients and real exponents) for which the unique positive equilibrium is a center.

The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.

Ecological communities can lose their permanence if a predator or a competitor is removed: the remaining species no longer coexist. This well-known phenomenon is analysed for some low dimensional examples of Lotka-Volterra type, with special attention paid to the occurrence of hetero-clinic cycles.

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

We focus on the long-term dynamics of "killing the winner" Lotka-Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.

In this paper, using the step method, we established the existence and uniqueness of solution for the system (1.2) with initial condition (1.3). The aim of this paper is to present a numerical method for this system. 1. The statement of the problem Consider the following Lotka-Volterra type delay differential system:  xi(t) = xi(t)ri(t) { ci − aixi(t)− n ∑

In the framework of Lotka-Volterra dynamics with evolutionary parameter variation, it is shown that a system of two competing species which is evolutionarily unstable, if left to themselves, is stabilized by a common predator preying on both of them. Game-theoretic implications of the results are also discussed.

In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.