Mathematical Models in Social Ecological Systems

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This case is an umbrella to capture a range of models of ecological, social, social-ecological, and other natural systems (e.g. climate).  In addition, there are several models whose main purpose is to demonstrate model visualization features related to a number of famous mathematical models including the Lorenz Model, the discrete logistic, and predator prey models. The Lorenz Model, probably the most famous of all simple models, is the first ever model of a chaotic dynamical system. Chaos arises when a deterministic, nonlinear dynamical systems exhibits a long-term unpredictability in behavior due to sensitivity to initial conditions. Lorenz (1963) provides the following overview of the model. 

Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.

The discrete logistic is another model, this time from population dynamics rather than atmoshperic dynamics, that exhibits chaotic dynamics.