We consider a generalized 1-D von Foerster equation. We present two discretization methods for the initial value problem and study stability of finite difference schemes on regular meshes.
For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...
We study stability switches for some class of delay differential equations with one discrete delay. We describe and use a simple method of checking the change of stability which originally comes from the paper of Cook and Driessche (1986). We explain this method on the examples of three types of prey-predator models with delay and compare the dynamics of these models under increasing delay.
In the present study the notion of watershed contour dynamics, defined within the framework of mathematical morphology, is examined. It is shown that the dynamics are a direct measure of the “sharpness” of transition between neighboring watershed basins. The expressions for the expected value and the statistical error of the estimation of contour dynamics are derived in the presence of noise, based on extreme value theory. The sensitivity of contour dynamics to noise is studied. A statistical approach...
Two species of animals are competing in the same environment. Under what conditions do they coexist peacefully? Or under what conditions does either one of the two species become extinct, that is, is either one of the two species excluded by the other? It is natural to say that they can coexist peacefully if their rates of reproduction and self-limitation are relatively larger than those of competition rates. In other words, they can survive if they interact strongly among themselves and weakly...
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner. Although the deterministic approach predicts (neutrally) stable coexistence of all species, for any finite population size, the intrinsic stochasticity unavoidably causes the eventual extinction of two of them.
An integral Markov operator appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let and be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence to are given.