SELF-ORGANIZED MARGINAL STABILITY RESULTING FROM INCONSISTENCY BETWEEN FUZZY-LOGIC AND DETERMINISTIC LOGIC - AN APPLICATION TO BIOLOGICAL-SYSTEMS

Complex systems in which internal agents (observers) interact with eac h other with finite velocity of information propagation cannot be desc ribed with a single consistent logic. We have proposed the bootstrappi ng system of cellular automata for describing such complex systems usi ng two types of complementary logic: Boolean and non-Boolean. We exten d this in this paper to a system of time-discrete continuous maps usin g fuzzy logic in place of non-Boolean logic. Fuzziness implies the int rinsic ambiguity of internal measurement. The bootstrapping system evo lves, changing the dynamics perpetually, so that the discrepancy betwe en the two types of complementary logic may be minimized. The equilibr ation force defined from the strength of discrepancy forms a landscape for self-organization which is similar to the fitness landscape for e volution. Though they appear similar, the former is derived from the i nternal dynamics. The goal of evolution, when applied to the map of th e Belousov-Zabochinsky reaction, is demonstrated to be near the border between periodicity and chaos. The behavior depends on the degree of fuzziness and the extent of noise. When fuzziness increases too much, the system becomes unstable. Near the boundary, it exhibits intermitte nt chaos with a background of 1/f noise. (C) 1997 Elsevier Science Ire land Ltd.