Park Jihoon, Mori Hiroki, Okuyama Yuji, Asada Minoru
Department of Adaptive Machine Systems, Graduate School of Engineering, Osaka University, Suita, Osaka, Japan.
Department of Intermedia Art and Science, School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan.
PLoS One. 2017 Aug 10;12(8):e0182518. doi: 10.1371/journal.pone.0182518. eCollection 2017.
Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.
混沌游走是一种非线性动力系统的状态在状态空间中自发探索并吸引某些状态的现象。从这个角度来看，动物的多样行为及其自发转变会导致一个复杂的耦合动力系统，包括身体和大脑。在此，我们进行了一系列模拟，使用不同类型的非线性振荡器网络（即规则网络、小世界网络、无标度网络、随机网络），并以肌肉骨骼模型（即蛇形机器人）作为身体，以了解身体行为的混沌游走是如何从身体与大脑之间的耦合动力学中产生的。然后对分类后的行为进行行为分析（行为聚类）和网络分析。前者包括从运动中提取特征向量以及对耦合动力学产生的运动模式进行分类。通过基于转移熵估计不同于给定非线性振荡器网络的“信息网络”，揭示分类运动模式背后的网络结构，转移熵用于发现神经元之间的信息流。实验结果表明：（1）运动模式的数量及其持续时间取决于控制身体与大脑动力学之间强度平衡的传感器比率以及给定非线性振荡器网络的类型；（2）利用复杂网络度量、聚类系数和最短路径长度，发现两种不同持续时间的运动模式背后存在两种信息网络，它们与运动模式的持续时间呈负相关和正相关。当前结果对于该方法未来扩展到更复杂的身体和环境似乎很有前景。还讨论了一些要求。
