Hiromichi Suetani

Detecting generalized synchronization between chaotic signals: a kernel-based approach

A unified framework for analysing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization, and dynamical change of the coupling strength between two chaotic systems can be captured by the proposed approach. It is also discussed how the kernel parameter is suitably chosen from data.

Chaotic phase synchronization in bursting-neuron models driven by a weak periodic force

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1:1 phase locking between a single spike and one period of the force and 1:l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramotos order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale.

Nonlinear structure of escape-times to falls for a passive dynamic walker on an irregular slope: Anomaly detection using multi-class support vector machine and latent state extraction by canonical correlation analysis

Falls that occur during walking are a significant problem from the viewpoints of both medicine and robotics engineering. It is very important to predict falls in order to prevent the falls or minimize the ensuing damage from them. In this study, we investigate the structure of the escape-times from walking to falling of a passive dynamic biped walker on a slope in a 2D plane with irregularities. We find that the structure lies on a manifold with high nonlinearity in state space that cannot be analyzed by linear methods under the assumption of a Gaussian distribution. Therefore, we first apply an extension of the support vector machine (SVM) to characterize its nonlinear structure, which enables us to predict imminent falls. Next, we find a latent space which describes the essential dynamics of the passive walker in a lower-dimensional space using canonical correlation analysis (CCA). There is wide applicability of this work for monitoring walking anomalies of both robots and human beings.

Self-Similarity Dynamics of On-Off Intermittency

We propose a new statistical law of on-offintermittency just after its onset in connection with the self-similarity dynamics which holds in a time region shorter than the correlation time. It is found that the coarse-grained variable averaged over the time region less than the correlation time takes a certain similarity form of probability density near the onset of intermittency. It is shown that the present statistics holds for several different systems, which suggests the existence of a new universality associated with on-offintermittency.

Using basin ruins and co-moving low-dimensional latent coordinates for dynamic programming of biped walkers on roughing ground

Disturbance rejection is one of the most important abilities required for biped walkers. In this study, we propose a method for dynamic programming of biped walking and apply it to a simple passive dynamic walker (PDW) on an irregular slope. The key of the proposed approach is to employ the transient dynamics of the walker just before approaching the falling state in the absence of any controlling input, and to derive the optimal control policy in the low-dimensional latent space. In recent our study, we found that such transient dynamics deeply relates to the basin of attraction for a stable gait. By patching latent coordinates to such a structures in each Poincaré section and defining the reward function according to the survive time of the transient dynamics, so-called escape-times, we construct a Markov decision process (MDP) for the PDW and obtain an optimal policy using a dynamic programming (DP). We will show that the proposed method actually succeeds in controlling the PDW even if the degree of disturbance is relatively large and the dimensionality of coordinates is reduced to lower ones.

A RANSAC-based ISOMAP for Filiform manifolds in nonlinear dynamical systems: an application to chaos in a dripping faucet

Trajectories generated from a chaotic dynamical system are lying on a nonlinear manifold in the state space. Even if the dimensionality of such a manifold is much lower than that of the full state space, we need many state variables to trace a motion on it as far as we remain to employ the original coordinate, so the resulting expression of the dynamics becomes redundant. In the present study, we employ one of the manifold learning algorithms, ISOMAP, to construct a new nonlinear coordinate that globally covers the manifold, which enables us to describe the dynamics on it as a low-dimensional dynamical system. Here, in order to improve the conventional ISOMAP, we propose an approach based on a combination with RANSAC for pruning the misconnected edges in the neighboring graph. We show that a clear deterministic relationship is extracted from time series of a mass-spring model for the chaotic dripping faucet using the proposed method.

PULSE DYNAMICS IN COUPLED EXCITABLE FIBERS: SOLITON-LIKE COLLISION, PHASE LOCKING, AND RECOMBINATION

We study the dynamics of a reaction–diffusion system composed of two mutually coupled excitable fibers. We focus on the situation in which dynamical properties of the two fibers are not identical because of the parameter difference between the fibers. Using the spatially one-dimensional FitzHugh–Nagumo equations as a model of a single excitable fiber, we show that the system exhibits a rich variety of dynamical behavior, including soliton-like collision between two pulses and recombination of a solitary pulse and synchronized pulses.

Deterministic stochastic resonance in chaotic diffusion

We show deterministic stochastic resonance (DSR) in chaotic diffusion when the diffusion map is modulated by a sinusoid. In chaotic diffusion, the map parameter determines the state transition rate and the diffusion coefficient. The transition rate shows the diffusion intensity. Therefore, the parameter represents the intensity of the internal fluctuation. By this fact, increase of the parameter maximizes the response of DSR as in standard stochastic resonance (SR) where the external noise intensity optimizes the response. Sinusoidally modulated diffusion is regarded as a stochastic process whose transition rate is modulated by the sinusoid. Therefore, the transition dynamics can be approximated by a time-dependent random walk process. Using the mean transition rate function against the map parameter, we can derive the DSR response depending on the parameter. Our approach is based on the rate modulation theory for SR. Even when the diffusion map is modulated by the sinusoid and noise from an external environment, the increasing parameter can also maximize the DSR response. We can calculate the DSR response depending on the external noise intensity and the map parameter. DSR takes advantage of applications to signal detection because the system has the control parameter corresponding to the internal fluctuation intensity.

Weak Sensitivity to Initial Conditions for Generating Temporal Patterns in Recurrent Neural Networks: A Reservoir Computing Approach

A function for generating temporal patterns such as melody of the music and motor commands for body movements is one of major roles in the brain. In this paper, we study how such temporal patterns can be generated from nonlinear dynamics of recurrent neural networks (RNNs) and clarify the hidden mechanism that supports the functional ability of RNNs from reservoir computing (RC) approach. We show that when the reservoir (random recurrent neural network) shows weak instability to initial conditions, the error of the output from the reservoir and the target pattern is sufficiently small and robust to noise. It is also shown that the output from the spontaneous activity of the trained system intermittently exhibits response-like activity to the trigger input, which may be related to recent experimental findings in the neuroscience.

Canonical correlation analysis for muscle synergies organized by sensory-motor interactions in musculoskeletal arm movements

Synergy is a key concept for understanding smooth and dexterous body movements generated in biological systems. In this paper, we propose an approach based on canonical correlation analysis (CCA) for identifying synergies that capture coherences organized between motor activations and sensory signals in movements. Using a musculoskeletal planar arm model with muscle and joint redundancies, we show that synergies identified by CCA give more natural and tractable activation patterns in virtual controller space with lower dimensionality when the arm performs reaching and a 3D pole balancing movement tasks.