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In this article, we study the global dynamics of a discrete two-dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this system. Moreover, we show that for a certain parameter range, there exists a compact interior attractor that attracts(More)
We derive models of the effects of periodic, discrete dosing or constant dosing of antibiotics on a bacterial population whose growth is checked by nutrient-limitation and possibly by host defenses. Mathematically rigorous results providing sufficient conditions for treatment success, i.e., the elimination of the bacteria, as well as for treatment failure,(More)
We develop a simple mathematical model of a bacterial colonization of host tissue which takes account of nutrient availability and innate immune response. The model features an infection-free state which is locally but not globally attracting implying that a super-threshold bacterial inoculum is required for successful colonization and tissue infection. A(More)
Biological systematics studies suggest that species are discretized in niche space. That is, rather than seeing a continuum of organism types with respect to continuous environmental variations, observers instead find discrete species or clumps of species, with one clump separated from another in niche space by a gap. Here, using a simple one dimensional(More)
A mathematical model of a mixed culture of bacteria in a fully three dimensional flow reactor which accounts for the colonization of the reactor wall surface by the microbes is studied both analytically and by simulation. It can be viewed as a model of the large intestine or of the fouling of a commercial bio-reactor or pipe flow. The primary focus is on(More)
We construct a Lyapunov function for a tridiagonal competitive-cooperative systems. The same function is a Lyapunov function for Kolmogorov tridiagonal systems, which are deened on a closed positive orthant in R n. We show that all bounded orbits converge to the set of equilibria. Moreover, we show that there can be no heteroclinic cycles on the boundary of(More)
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