International Encyclopedia of Systems and Cybernetics

Condition of a system or process led by a fluctuation of a critical variable out of its homeostatic stability channel.

Dynamic stability's main characteristic is that the system oscillates periodically within defined limits of amplitude, without ever leaving the established fluctuations channel, or domain of attraction.

Instability, on the contrary is a runaway process with a finite time course, through a succesion of ever amplifying oscillations which lead the system closer and closer to the limits of its stability channel until a critical threshold is neared and the process undergoes a basic change. At that point the system reaches metastability and the slightest supplementary disturbance – even a small random "push" – turns it unstable, destroys it (the most common case for individual systems) or, rarely, shifts it toward a different form or organization.

Instability is closely related to environmental conditions, as stated by R. FIVAZ: "… instabilities have the property to bind conditionally the internal structure of the system to the value of an external field. This conditional bind is certainly a necessary ingredient to construct a complex system modelization inasmuch as such systems interact with the outside constantly, albeit selectively.

"In addition, real situations are characterized by unpredictable variations in the environment which submit systems to a succesion of independent and random fields" (1991, p.22).

The most significant perturbing influence for a system is a high increase of the rate of energy intake, which is the factor that leads it to giant fluctuations. In human systems, such increase is induced by the system itself (technical advances in the captation and uses of energy).

More recently, the boundaries of stability and instability have become quite blurred, through our new understanding of deterministic chaos. It becomes rather difficult in the case of a nonlinear system to know if it is inherently stable, metastable or unstable, since it may fluctuate wildly and frequently bifurcate, with the possibility that it may cross an instability threshold.

In some cases, the concept of instability should however be relativized. According to C. HOLLING, many systems have alternative dynamic stability conditions, within more global conditions of stability, as they may leap from one domain of attraction into another under the impact of some very strong and unusual perturbation. HOLLING writes: "… many examples for the influence of random events upon natural systems… suggest that instability, in the sense of large fluctuations, may introduce a resilience and a capacity to persist. They point out the very different view of the world that can be obtained if we concentrate on the boundaries to the domain of attraction rather than on equilibrium states. Although the equilibrium-centered view is analytically more tractable, it does not always provide a realistic understanding of the system's behavior" (1976, p.81).

In such cases, we could possibly speak of an endogenous ergodic instability. While unstable, the system at least keeps its identity.

An interesting comment by Y. SINAI connects instability with randomness: "The more unstable the movement, the more stable become the manifestations of randomness. The instability of a non-aleatory dynamics leads to the rise of randomness" (1992, p.87).