By George J. Klir (Eds.)
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Additional info for Foundations of Mathematical System Dynamics. The Fundamental Theory of Causal Recursion and Its Application to Social Science and Economics
19) on the torus. The question of the possible real-world examples will be discussed in the following section. 5 Irregularly ( ' C h a o t i c a l l y ' ) Pulsating Selfregulating Systems Again we are concerned with positively Poisson-stable motions along quasiclosed curves on a non-trivial attractor limit set, or motions of state tending to such motions from outside the attractor limit set. 18) on the torus of Fig. 12. If, instead of the uniform motion of state, Eq. 20) =Αψ9χ), 9 where / is a continuous and positive-valued function, we have an example of what is called an irregular or 'chaotic motion of state.
16. 6557Î (the lower figure), (b) Mandelbrot's set of the parameter values c for which the Julia attractor sets are connected, (c) A detail from the 'tail of the seahorse' in Picture (b). ) xR+ itself, recede to infinity with t -> + oo, and all their points have empty positive limit sets. (Note that the unbounded trajectory with the non-empty positive limit set in Fig. ) This explains the scarcity of mathematical results concerning self-steering, as most recent research in dynamics has been focused on attractor limit sets, and thus on self-regulating systems.
7 below, it is necessary to limit the interpretation so that what is self-steering in the human mind is the total intellectual process. Not all partial processes need be self-steering. Real-world Examples (Human Development, Social Interaction). The intellectual total process in the human brain is the ultimate source of human development and the basis of all social interaction between human beings. Hence, self-steering has been proposed to play a prominent role in the conceptual foundations of social science (Aulin, 1982, 1985, 1986a, 1987b; Geyer and van der Zouwen, 1986).