Ito K, Gunji Y P
Faculty of Science, Graduate School of Science and Technology, Kobe University, Japan.
Biosystems. 1997;41(3):179-90. doi: 10.1016/s0303-2647(96)01672-3.
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.
在内部主体（观察者）以有限信息传播速度相互作用的复杂系统中，无法用单一的一致逻辑来描述。我们提出了细胞自动机的自引导系统，用于使用两种互补逻辑（布尔逻辑和非布尔逻辑）来描述此类复杂系统。在本文中，我们将其扩展为一个时间离散连续映射系统，用模糊逻辑代替非布尔逻辑。模糊性意味着内部测量的固有模糊性。自引导系统不断演化，持续改变动力学，以使两种互补逻辑之间的差异最小化。由差异强度定义的平衡力形成了一个自组织景观，类似于进化的适应度景观。尽管它们看起来相似，但前者源自内部动力学。当应用于贝洛索夫 - 扎博廷斯基反应的映射时，进化的目标被证明接近周期性和混沌之间的边界。行为取决于模糊度和噪声程度。当模糊度增加过多时，系统变得不稳定。在边界附近，它表现出以1/f噪声为背景的间歇性混沌。
