We postulate that reasonable notions of sustainability must include a time-scale synchronization of both the processes of human development and those of the natural environment. We perform our analysis within a simple system of five differential equations where non-renewable and renewable resources are coupled with production capacities, abatement and human capital as functions of time. A 'sustainability screw' phenomenon is demonstrated describing a spiral like trajectory of three key variables-the non-renewable resources, the renewable resources and the production capital. This spiral may tend to an undesirable steady state, however, by adjusting a ratio of intensity parameters, time scales of production and natural recovery processes can be altered to produce more sustainable trajectories.
- multiple time scale
- Sustainable optimization systems