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R. A. Desharnais, B. Dennis, J. M. Cushing, S. M. Henson and R. F. Costantino, “Chaos and Population Control of Insect Outbreaks,” Ecology Letters, Vol. 4, No. 3, 2001, pp. 229-235. http://dx.doi.org/10.1046/j.1461-0248.2001.00223.x

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.