Nara Shigetoshi
Department of Electrical and Electronic Engineering, Faculty of Engineering, Okayama University, 700-8530 Okayama, Japan.
Chaos. 2003 Sep;13(3):1110-21. doi: 10.1063/1.1604251.
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.
从复杂动力学在包括大脑在内的生物系统的复杂功能和控制中以及在自然界的复杂结构形成中发挥重要作用的观点出发，我们考虑具有大但有限自由度的系统中的复杂动力学，包括混沌。作为其中的一个例子，展示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，例如通过计算神经元之间的相关函数、混沌动力学的盆地访问度量等，研究状态空间中的不稳定性、遍历性或局域化。作为使用这种复杂动力学进行功能实验的一个例子，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。我们将这种有用的动力学称为“受限混沌”，它也可能被称为“混沌遍历”。这些结果表明，受限混沌在具有大但有限自由度的系统的复杂功能和控制中可能具有潜在用途，这些系统通常在生物系统中观察到，并且可能是这样的，即在高维状态空间中根据给定的情况、环境和要控制或处理的上下文，在收敛动力学和发散动力学之间以微妙的平衡工作。
