We show, within the context of the standard class of deterministic ODE predator-prey mathematical models, that predator culling does not produce a long term decrease in the predator population.

A ‎nonstandard finite difference (NSFD) scheme has been constructed and analyzed for a mathematical model that describes Lotka–Volterra food web model‎. ‎This new discrete system has the same stability properties as the continuous model and,‎on the whole‎, ‎it preserves‎the same local asymptotic stability properties‎. ‎Linearized stability theory and Schur–Cohn criteria are used for local asymp...

This paper is concerned with a cooperative two-species Lotka–Volterra model. Using the fixed point theorem, the existence results of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions are obtained. Our results show that this model possesses at least one coexistence state if the birth rates are big and cross-diffusions are suitably weak. c © 2007 Elsev...

...................................................................................................................3 Research Project Background.............................................................................4 -Predator-Prey Interaction -Natural Selection and Coevolution -The Test Case: Canadian Lynx and Snowshoe Hare Laying a Foundation in Differential Equations......................

6 Winnerless competition is a theoretical model used to study cognitive and 7 attention-based processes using the sequential switching between 8 metastable states of a neurodynamical system. This competition is observed 9 in both physical neural networks and in higher-ordered cognition. I 10 demonstrate this principle in a network of three interconnected Fitzhugh11 Nagumo neurons and in the wor...

A resource based ecological competition model with interference is proposed. The model is based on Lotka-Volterra dynamics with two predators competing for a single, limited prey. Interference effects are considered in this article. When the interference coefficient, expressing the damage effect from its rival, is small, the mathematical analysis shows that the winner in purely exploitative com...

Self-replicating malicious codes (worms) are striking the Internet vigorously. A particularly interesting trend is the emergence of mutually agnostic virus. In this work we study such combating virus system. Like other virus models, we also present an adapted version of Lotka-Volterra equation model to show the interaction dynamics of mutually antagonistic selfspreading codes. There are few nov...

Abstract: Based on the work by Smirnov and Zeitlin, we study a simple realization of the matrix construction of the affine Jacobi varieties. We find that the realization is given by a classical integrable model, the extended Lotka-Volterra lattice. We investigate the integrable structure of the representative for the gauge equivalence class of matrices, which is isomorphic to the affine Jacobi ...

We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law distribution of intervals between extinctions, but only for ecosystems with sufficient variability of species and with networks of connectivity above certain threshold ...