Any system with various simultaneously interacting causal lines that impede rigorous globally deterministic behavior.
L. DOUGLAS KIEL writes: "Linear systems respond to minimal changes in their parameters, or to external shocks, in a smooth and proportionate manner" (1992, p.30).
It is really very difficult to conceive a system which would be truly linear. Models of systems are frequently linear, indeed. But their reliability is generally limited to a small and short term range of the system's behavior.
DOUGLAS KIEL writes: "A small change in a nonlinear system can, however, produce an enormous difference in the structure and behavior of the system" (Ibid).
However, many small changes have no such effects, with the result that we may well believe in a non-existant long term dynamic (or even static!) stability.
"…external disturbances may amplify nonlinear interactions, generating instabilities, that may initiate a break with the pre-existing behavioral and structural regimes" (Ibid).
"Nonlinear systems may also reveal a "sensitive dependence on initial conditions" (J. GLEICK, 1987).
"A small difference in the initial conditions of seemingly similar nonlinear systems can lead to dramatically different evolutionary paths and outcomes….Any effort at forecasting the behavior of a nonlinear system is, thus a highly suspect activity" (Ibid).
This is possibly somewhat over-pessimistic: With good monitoring, a sufficient grasp of chaos theory, and as much as possible consolidated knowledge of the various levels of cyclical activity of the system, some forecasting is feasible… but the results should always be taken with caution.
According to DOUGLAS KIEL: "Nonlinear systems exhibit four distinct types of temporal behavior…
1) convergence to a stability or equilibrium
2) stable oscillation
3) unstable and explosive
Each regime can appear within the long term behavior of a nonlinear system" (Ibid).
Another important aspect is, in P.M. ALLEN et al. words: "…nonlinear systems, operating far from thermodynamic equilibrium, can undergo successive structural instabilities leading to a progressive complexification of their organization and functioning. Such phenomena involve a dialogue between stochastic and deterministic aspects of the system, as the interaction tend to a "self-organization" process of successive periods of stability and instability, where new qualities, traits and characteristic emerge over time" (1984, p.150).
Evolution seems thus to offer a "punctuated" character, as claimed in living systems by GOULD and ELDREDGE.
- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
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To cite this page, please use the following information:
Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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