Observation of a Fast Rotating Wave in Rings of Coupled Chaotic Oscillators

Abstract

We report on the discovery of a transition in rings of coupled electronic circuits in the chaotic regime to a collective periodic state characterized by a time scale that is between two and three orders faster than that corresponding to an isolated circuit. This transition arises from a linear instability in the uniform synchronized state of the ring through a symmetric Hopf bifurcation. The same type of transition is also observed for other coupled chaotic systems, e.g., a ring of Lorenz attractors.

Inverse Proportional Relationship Between Switching-Time Length and Fractal-Like Structure for Continuous Tracking Movement

“…Recent studies have confirmed that fractal-like and self-similar structures exist not only in various physical phenomena [Arecchi et al, 1986;Constantin et al, 1991;Mestl et al, 1997;Maas et al, 1997;Matias et al, 1997;Schmiegel & Eckhardt, 1997;Tanii et al, 1999;Tanii et al, 1991] but also in human motor control in cases when we switch several movement patterns rapidly with a particular switching-time length T [Yamamoto & Gohara, 2000] or several T s [Suzuki & Yamamoto, 2015]. Moreover, we confirmed the inverse proportional relationship between T and the fractal-like feature D 2 in human pointing movement [Hirakawa et al, 2016].…”

“…this is considered an excited attractor. Recent studies based on this dynamical systems theory, for example not only the physical phenomenon [Arecchi et al, 1986;Constantin et al, 1991;Maas et al, 1997;Matias et al, 1997;Mestl et al, 1997;Schmiegel & Eckhardt, 1997;Tanii et al, 1999;Tanii et al, 1991] but also human movement [Hirakawa et al, 2016;Suzuki & Yamamoto, 2015;Yamamoto & Gohara, 2000], have revealed that the spatiotemporal structure in various natural phenomena is fractal-like and/or self-similar. These studies on human movement entailed tasks in which participants switched several different movement patterns continuously with the external inputs being abruptly switched.…”

Switching Dynamics Between Two Movement Patterns Varies According to Time Interval

“…This implies that we should not assume that only one system is involved in human motor control and that we should consider the relationships between subsystems and the environment. Such phenomena have also been observed in various physical manifestations other than human movement, such as optical systems [Arecchi et al, 1986;Tanii et al, 1991Tanii et al, , 1999, turbulence [Constantin et al, 1991;Maas et al, 1997;Schmiegel & Eckhardt, 1997] and electronic circuits [Matias et al, 1997;Mestl et al, 1997]. This subsystem in human motor control corresponds to a movement pattern, and the behavioral output of this pattern by the subsystem is from an attractor.…”

Desynchronization Transitions in Rings of Coupled Chaotic Oscillators

“…In this situation it was observed [Matías et al, 1997a] that the synchronized chaotic state is stable if the size of the ring is small enough, e.g. N = 2 (see Fig.…”