T. Awerbuch, R. Levins and M. Predescu, “Co-Dynamics of Consciousness and Populations of the Dengue Vector in a Spraying Interventions System Modeled by Difference Equations,” Far East Journal of Applied Mathematics, Vol. 37, No. 2, 2009, pp. 215-228.

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.