Can potentially useful dynamics to solve complex problems emerge from constrained chaos and/or chaotic itinerancy?
Can potentially useful dynamics to solve complex problems emerge from constrained chaos and/or chaotic itinerancy?
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作者：
S. Nara
从包括脑在内的生物系统的复杂功能和控制，以及自然界中复杂的结构形成的角度，考虑了大但有限自由度系统中的包括混沌在内的复杂动力学。作为例子，给出了在递归神经网络模型中发生的复杂动力学的计算机实验。通过数值分析来研究状态空间中的不稳定性、巡回性或局部性，例如通过计算神经元之间的关联函数、混沌动力学的流域访问度量等。作为使用这种复杂动力学的功能实验的例子，我们展示了在典型的不适定背景下执行记忆搜索任务的结果。我们把这种有用的动力学称为“受限混沌”，也可以称为“混沌巡游”。这些结果表明，对于通常在生物系统中观察到的具有大但有限自由度的系统的复杂功能和控制，约束混沌可能是有用的，并且可能工作在高维状态空间中的收敛动力学和发散动力学之间的微妙平衡，这取决于给定的情况、环境和要控制或要处理的上下文。
Complex dynamics including chaos in systems with large but finite degrees of freedom are considered from the viewpoint that they would play important roles in complex functioning and controlling of biological systems including the brain, also in complex structure formations in nature. As an example of them, the computer experiments of complex dynamics occurring in a recurrent neural network model are shown. Instabilities, itinerancies, or localization in state space are investigated by means of numerical analysis, for instance by calculating correlation functions between neurons, basin visiting measures of chaotic dynamics, etc. As an example of functional experiments with use of such complex dynamics, we show the results of executing a memory search task which is set in a typical ill-posed context. We call such useful dynamics "constrained chaos," which might be called "chaotic itinerancy" as well. These results indicate that constrained chaos could be potentially useful in complex functioning and controlling for systems with large but finite degrees of freedom typically observed in biological systems and may be such that working in a delicate balance between converging dynamics and diverging dynamics in high dimensional state space depending on given situation, environment and context to be controlled or to be processed.