108 research outputs found
Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average
We present a general framework of detrending methods of fluctuation analysis
of which detrended fluctuation analysis (DFA) is one prominent example. Another
more recently introduced method is detrending moving average (DMA). Both
methods are constructed differently but are similarly able to detect long-range
correlations as well as anomalous diffusion even in the presence of
nonstationarities. In this article we describe their similarities in a general
framework of detrending methods. We establish this framework independently of
the definition of DFA or DMA but by investigating the failure of standard
statistical tools applied on nonstationary time series, let these be intrinsic
nonstationarities such as for Brownian pathes, or external ones due to additive
trends. In particular, we investigate the sample averaged mean squared
displacement of the summed time series. By modifying this estimator we
introduce a general form of the so-called fluctuation function and can
formulate the framework of detrending methods. A detrending method provides an
estimator of the fluctuation function which obeys the following principles: The
first relates the scaling behaviour of the fluctuation function to the
stochastic properties of the time series. The second principles claims
unbiasedness of the estimatior. This is the centerpiece of the detrending
procedure and ensures that the detrending method can be applied to
nonstationary time series, e.g. FBM or additive trends. Both principles are
formulated and investigated in detail for DFA and DMA by using the relationship
between the fluctuation function and the autocovariance function of the
underlying stochastic process of the time series
Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing
The stabilization of an inverted pendulum on a manually controlled cart (cart-inverted-pendulum; CIP) in an upright position, which is analogous to balancing a stick on a fingertip, is considered in order to investigate how the human central nervous system (CNS) stabilizes unstable dynamics due to mechanical instability and time delays in neural feedback control. We explore the possibility that a type of intermittent time-delayed feedback control, which has been proposed for human postural control during quiet standing, is also a promising strategy for the CIP task and stick balancing on a fingertip. Such a strategy hypothesizes that the CNS exploits transient contracting dynamics along a stable manifold of a saddle-type unstable upright equilibrium of the inverted pendulum in the absence of control by inactivating neural feedback control intermittently for compensating delay-induced instability. To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors. We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing. We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy
Picture of the low-dimensional structure in chaotic dripping faucets
Chaotic dynamics of the dripping faucet was investigated both experimentally
and theoretically. We measured continuous change in drop position and velocity
using a high-speed camera. Continuous trajectories of a low-dimensional chaotic
attractor were reconstructed from these data, which was not previously obtained
but predicted in our fluid dynamic simulation. From the simulation, we further
obtained an approximate potential function with only two variables, the drop
mass and its position of the center of mass. The potential landscape helps one
to understand intuitively how the dripping dynamics can exhibit low-dimensional
chaos.Comment: 8 pages, 3 figure
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