stability

Stability

Stability is a very old notion. 

Formal study of stability can be attributed to ancient astronomers and priests from numerous civilizations as they studied the predictability of the celestial objects and natural cycles. Currently, there are very many formulations of stability. Even in the mid-1980s, Szebehely (1984) suggested at least 50 different usages in existence within the field of celestial mechanics alone (although most related to different ways of measuring or indexing similar concepts). 

There seem to be two main classes of stability concepts that relate to: 

• • a global boundedness of a system (Lagrangian orbital stability)

• a local asymptotic (Liapunov sensitivity to small perturbations)

Both are important and not necessarily the same. For example, an orbit can be stable in the global, bounded sense and yet be unstable in the local sense. 

The awareness of the three-body-problem in physics drove home the point that:

• • even the simplest of systems are highly likely to demonstrate truly bewildering dynamical complexity, and 

• the capacity of the form of this dynamical complexity to change dramatically with even slightly different parameterizations of the very same system (i.e., bifurcation phenomenon, semi-stability and transient effects associated with changes in external and/or internal constraints, energy gradient, space-time structure).

The need for a complete re-think on the nature of stability was evident. It is currently an ongoing process that is still in its infancy. 

Add to this the complex and mutli-dimensional nature of ecological systems and one can but expect the current  perplexedness of most ecologists on the notion of stability (myself included!). Everyone has an opinion but no-one agrees. In ecology, there are also many variants of stability (in meaning and measurement) although perhaps not as many as in celestial mechanics. 

References

Szebehely, V. 1984.  Review of concepts of stability. Celestial Mechanics 34:49-64.