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.