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M. Krkosek, M. A. Lewis, A. Morton, L. N. Frazer and J. Volpe, “Epizootic of Wild Fish Induced by Farm Fish,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 103, No. 42, 2006, pp. 15506-15510. http://dx.doi.org/10.1073/pnas.0603525103

has been cited by the following article:

• TITLE: Managing Populations with Unimodal Dynamics

  AUTHORS: Richard Levins, Tamara Awerbuch, Hyung Park

  KEYWORDS: Qualitative Analysis; Difference Equations; Unimodal Dynamics; Intervention Strategies; Chaos; Li-Yorke Criterion; Pest Management; Species Enrichment; Pre-Image Sets

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10B, October 4, 2013

  ABSTRACT: In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equation, X n+1 = f ( X n ), are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos we propose a qualitative intervention rule that can be applied without any explicit population equation. This proposed strategy for intervention brings out many interesting behaviors in population dynamics. A qualitative decision rule can be applied with a straight edge without any population equation and therefore offers a robust strategy for the management of populations.