TY - JOUR

T1 - Self-organized marginal stability resulting from inconsistency between fuzzy logic and deterministic logic

T2 - An application to biological systems

AU - Ito, Keisuke

AU - Gunji, Yukio Pegio

PY - 1997/2/1

Y1 - 1997/2/1

N2 - Complex systems in which internal agents (observers) interact with each other with finite velocity of information propagation cannot be described with a single consistent logic. We have proposed the bootstrapping system of cellular automata for describing such complex systems using two types of complementary logic: Boolean and non-Boolean. We extend this in this paper to a system of time-discrete continuous maps using fuzzy logic in place of non-Boolean logic. Fuzziness implies the intrinsic ambiguity of internal measurement. The bootstrapping system evolves, changing the dynamics perpetually, so that the discrepancy between the two types of complementary logic may be minimized. The equilibration force defined from the strength of discrepancy forms a landscape for self-organization which is similar to the fitness landscape for evolution. Though they appear similar, the former is derived from the internal dynamics. The goal of evolution, when applied to the map of the 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 intermittent chaos with a background of 1/f noise.

AB - Complex systems in which internal agents (observers) interact with each other with finite velocity of information propagation cannot be described with a single consistent logic. We have proposed the bootstrapping system of cellular automata for describing such complex systems using two types of complementary logic: Boolean and non-Boolean. We extend this in this paper to a system of time-discrete continuous maps using fuzzy logic in place of non-Boolean logic. Fuzziness implies the intrinsic ambiguity of internal measurement. The bootstrapping system evolves, changing the dynamics perpetually, so that the discrepancy between the two types of complementary logic may be minimized. The equilibration force defined from the strength of discrepancy forms a landscape for self-organization which is similar to the fitness landscape for evolution. Though they appear similar, the former is derived from the internal dynamics. The goal of evolution, when applied to the map of the 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 intermittent chaos with a background of 1/f noise.

KW - Edge of chaos

KW - Fuzzy set

KW - Measurement

KW - Self-organization

UR - http://www.scopus.com/inward/record.url?scp=0030620060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030620060&partnerID=8YFLogxK

U2 - 10.1016/S0303-2647(96)01672-3

DO - 10.1016/S0303-2647(96)01672-3

M3 - Article

C2 - 9113352

AN - SCOPUS:0030620060

SN - 0303-2647

VL - 41

SP - 179

EP - 190

JO - Currents in modern biology

JF - Currents in modern biology

IS - 3

ER -