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A nonlinear threshold model for community response to environmental hazards 

Author: L. A. Zager a
Affiliation:   a Massachusetts Institute of Technology, Cambridge, MA, USA
DOI: 10.1080/10236190701434122
Publication Frequency: 12 issues per year
Published in: journal Journal of Difference Equations and Applications, Volume 13, Issue 11 November 2007 , pages 1065 - 1078
First Published: November 2007
Formats available: HTML (English) : PDF (English)
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Abstract

In Predescu et al. 2002, the authors present a model for the interaction between the number of mosquito breeding sites in a community and that community's “level of consciousness” of the environmental problem. We build upon this concept here by generalizing the model and incorporating a threshold relationship between the environmental hazard, ./GDEA_A_243294_O_XML_IMAGES/GDEA_A_243294_O_ILM0001.gif , and community response, ./GDEA_A_243294_O_XML_IMAGES/GDEA_A_243294_O_ILM0002.gif ; the hazard must exceed a critical level ω before a community intervenes../GDEA_A_243294_O_XML_IMAGES/GDEA_A_243294_O_UM0001.gif The model exhibits three different regimes of behavior as a function of the parameters: a zero-consciousness equilibrium, a positive consciousness (and low hazard) regime, and an oscillatory intermediate regime. This paper establishes global and local stability results, characterizations of trajectories and invariant regions of phase space for each of the regimes, and presents a complete characterization of the behavior of the special case in which community awareness increases at a constant rate once the threshold is reached.
Keywords: 39A11; 40A05
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