Hal Smith

Publications (2)0 Total impact

• Source

  Available from: ArXiv

  Article: Global dynamics of a discrete two-species Lottery-Ricker competition model.

  Yun Kang, Hal Smith
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  ABSTRACT: 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 all interior points except Lebesgue measure zero set. This result gives a weaker form of coexistence which is referred to as relative permanence. This new concept of coexistence combined with numerical simulations strongly suggests that the basin of attraction of the locally asymptotically stable interior period-2 orbit is an infinite union of connected components. This idea may apply to many other ecological models. Finally, we discuss the generic dynamical structure that gives relative permanence.
  Journal of Biological Dynamics 03/2012; 6(2):358-76.
• Source

  Available from: psu.edu

  Article: The Pharmacodynamics of Antibiotic Treatment

  Imran Mudassar, Hal Smith
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  ABSTRACT: 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, are obtained. Our models can exhibit bi-stability where the infection-free state and an infection-state are locally stable when antibiotic dosing is marginal. In this case, treatment success may occur only for sub-threshold level infections.