Dynamic landscapes, stability and ecological modeling.

The image of a ball rolling along a series of hills and valleys is an effective heuristic by which to communicate stability concepts in ecology. However, the dynamics of this landscape model have little to do with ecological systems. Other landscape representations, however, are possible. These include the particle on an energy landscape, the potential landscape, and the Lyapunov function landscape. I discuss the dynamics that these representations admit, and the application of each to ecological modeling and the analysis and representation of stability.