Dynamical behaviors in the FitzHugh–Nagumo system with a memory trace

In this paper, the dynamical behaviors of the FitzHugh–Nagumo (FHN) system with a memory trace, which has time-fractional derivatives, are investigated. For the case of a classical order, the constant input current can change the stability of the equilibrium point in a single FHN unit, and the equilibrium is unstable in a certain range of the current. A decrease of the order of the time-fractional derivative may lead to a linear reduction of the range and the appearance of a solution of mixed-mode oscillations, which consist of subthreshold small-amplitude oscillation and suprathreshold large-amplitude oscillation. In the parameter space of the input current and the fractional order, the region of existing the mixed-mode oscillation is linearly widened when the fractional order moves toward its small value. If a suprathreshold perturbation is periodically applied, there exist some obvious bands, on which the excited period is locked to the perturbation period according to some rational ratios. As a result, the bands can be narrowed by decreasing the value of fractional order and their location has a slight drift toward the small value of the perturbation period. In addition, the properties of solitary traveling waves and wave train solutions are also studied in the one-dimensional space. It is illustrated that the traveling pulse is wider for a smaller value of fractional order, and its velocity is larger. Further, some relations of wave trains have a great change when the value of the fractional order is changed.

Aging Affects Lower Limb Joint Moments and Muscle Responses to a Split-Belt Treadmill Perturbation

Age-related changes cause more fall-related injuries and impede the recoveries by older adults compared to younger adults. This study assessed the lower limb joint moments and muscle responses to split-belt treadmill perturbations in two groups (14 healthy young group [23.36 ± 2.90 years] and 14 healthy older group [70.93 ± 4.36 years]) who performed two trials of unexpected split-belt treadmill perturbations while walking on a programmable split-belt treadmill. A motion capture system quantified the lower limb joint moments, and a wireless electromyography system recorded the lower limb muscle responses. The compensatory limb's (i.e., the tripped limb's contralateral side) joint moments and muscle responses were computed during the pre-perturbation period (the five gait cycles before the onset of a split-belt treadmill perturbation) and the recovery period (from the split-belt treadmill perturbation to the baseline gait relying on the ground reaction forces' profile). Joint moments were assessed by maximum joint moments, and muscle responses were quantified by the normalization (%) and co-contraction index (CCI). Joint moments and muscle responses of the compensatory limb during the recovery period were significantly higher for the YG than the OG, and joint moments (e.g., knee flexion and extension and hip flexion moments) and muscle responses during the recovery period were higher compared to the pre-perturbation period for both groups. For CCI, the older group showed significantly higher co-contraction for biceps femoris/rectus femoris muscles than the young group during the recovery period. For both groups, co-contraction for biceps femoris/rectus femoris muscles was higher during the pre-perturbation period than the recovery period. The study confirmed that older adults compensated for muscle weakness by using lower joint moments and muscle activations and increasing muscle co-contractions to recover balance after split-belt treadmill perturbations. A better understanding of the recovery mechanisms of older adults who train on fall-inducing systems could improve therapeutic regimens.

Evolutionary Search for Cellular Automata with Self-Organizing Properties toward Controlling Decentralized Pervasive Systems and Its Applications

Cellular Automata (CAs) have been investigated extensively as abstract models of the decentralized systems composed of autonomous entities characterized by local interactions. However, it is poorly understood how CAs can interact with their external environment, which would be useful for implementing pervasive systems that consist of billions of components (nodes, sensors, etc.). This paper focuses on the emergent properties of CAs induced by external perturbations toward controlling pervasive systems. The authors assumed a minimum task in which a CA has to change its global state drastically after every occurrence of a perturbation period. By conducting evolutionary searches for rules of CAs, they obtained interesting behaviors of CAs in which their global state cyclically transited among different stable states in either ascending or descending order. They analyze the emergent behavior in detail and also introduce applications of the evolved CA for controlling pervasive robots and an interactive art.

Evolutionary Search for Cellular Automata with Self-Organizing Properties toward Controlling Decentralized Pervasive Systems

Cellular Automata (CAs) have been investigated extensively as abstract models of the decentralized systems composed of autonomous entities characterized by local interactions. However, it is poorly understood how CAs can interact with their external environment, which would be useful for implementing decentralized pervasive systems that consist of billions of components (nodes, sensors, etc.) distributed in our everyday environments. This chapter focuses on the emergent properties of CAs induced by external perturbations toward controlling decentralized pervasive systems. We assumed a minimum task in which a CA has to change its global state drastically after every occurrence of a perturbation period. In the perturbation period, each cell state is modified by using an external rule with a small probability. By conducting evolutionary searches for rules of CAs, we obtained interesting behaviors of CAs in which their global state cyclically transited among different stable states in either ascending or descending order. The self-organizing behaviors are due to the clusters of cell states that dynamically grow through occurrences of perturbation periods. These results imply that we can dynamically control the global behaviors of decentralized systems by states of randomly selected components only.

Generation of Torsional Oscillations in the Sun

The hypothesis is considered that the torsional wave observed on the Sun is an eigenmode oscillation excited in the presence of a weak poloidal magnetic field. We derive asymptotic linear equations for a perturbation with a large number of nodes along the radius, assuming the rotation to be slow and the characteristic perturbation period to be much longer than the rotational period. The results of a preliminary numerical study of the stability of the torsional mode indicate that the superadiabaticity of the solar convection may contribute to the excitation of this mode. In the present work the approximation of harmonic radial dependence of the perturbation has been used.