A general converging point in a three dimensional chaotic attractor.
The saddle is formed by two overlapping fractal structures, the inset and the outset of an unstable solution.
The central point C of the saddle is common to the stable manifold of the system and to its unstable one.
As the saddle implies convergence, it is easier to stabilize a chaotic system by application of small corrections (or perturbations) when the chaotic trajectory passes near its central point (D. BROOMHEAD, 1990, p.23).
St. KAUFFMAN writes: "… saddle steady states are stable with respect to perturbations in some directions, and unstable with respect to perturbations in other directions. The existence of saddles reflects the fact that two stable basins of attraction must abut, and the ridge where they do is a basin of attraction having one fewer dimension that the number of variables in the system and is called a separatrix"(1993, p.177).
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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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