A nonlinear threshold model for community response to environmental hazards

摘要

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, x(n), and community response, z(n); the hazard must exceed a critical level omega before a community intervenes. [GRAPHICS] 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.