TY - JOUR

T1 - Spontaneous switching among multiple spatio-temporal patterns in three-oscillator systems constructed with oscillatory cells of true slime mold

AU - Takamatsu, Atsuko

N1 - Funding Information:
The author thanks Professor T. Fujii, of IIS, The University of Tokyo, for his assistance, that of members of this laboratory in microfabrication, Professor N. Murata, Waseda University, for his useful suggestions on statistical analysis. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and a Waseda University Grant for Special Research Projects.

PY - 2006/11/15

Y1 - 2006/11/15

N2 - Three-oscillator systems with plasmodia of true slime mold, Physarum polycephalum, which is an oscillatory amoeba-like unicellular organism, were experimentally constructed and their spatio-temporal patterns were investigated. Three typical spatio-temporal patterns were found: rotation (R), partial in-phase (P I), and partial anti-phase with double frequency (P A). In pattern R, phase differences between adjacent oscillators were almost 120{ring operator}. In pattern P I, two oscillators were in-phase and the third oscillator showed anti-phase against the two oscillators. In pattern P A, two oscillators showed anti-phase and the third oscillator showed frequency doubling oscillation with small amplitude. Actually each pattern is not perfectly stable but quasi-stable. Interestingly, the system shows spontaneous switching among the multiple quasi-stable patterns. Statistical analyses revealed a characteristic in the residence time of each pattern: the histograms seem to have Gamma-like distribution form but with a sharp peak and a tail on the side of long period. That suggests the attractor of this system has complex structure composed of at least three types of sub-attractors: a "Gamma attractor"-involved with several Poisson processes, a "deterministic attractor"-the residence time is deterministic, and a "stable attractor"-each pattern is stable. When the coupling strength was small, only the Gamma attractor was observed and switching behavior among patterns R, P I, and P A almost always via an asynchronous pattern named O. A conjecture is as follows: Internal/external noise exposes each pattern of R, P I, and P A coexisting around bifurcation points: That is observed as the Gamma attractor. As coupling strength increases, the deterministic attractor appears then followed by the stable attractor, always accompanied with the Gamma attractor. Switching behavior could be caused by regular existence of the Gamma attractor.

AB - Three-oscillator systems with plasmodia of true slime mold, Physarum polycephalum, which is an oscillatory amoeba-like unicellular organism, were experimentally constructed and their spatio-temporal patterns were investigated. Three typical spatio-temporal patterns were found: rotation (R), partial in-phase (P I), and partial anti-phase with double frequency (P A). In pattern R, phase differences between adjacent oscillators were almost 120{ring operator}. In pattern P I, two oscillators were in-phase and the third oscillator showed anti-phase against the two oscillators. In pattern P A, two oscillators showed anti-phase and the third oscillator showed frequency doubling oscillation with small amplitude. Actually each pattern is not perfectly stable but quasi-stable. Interestingly, the system shows spontaneous switching among the multiple quasi-stable patterns. Statistical analyses revealed a characteristic in the residence time of each pattern: the histograms seem to have Gamma-like distribution form but with a sharp peak and a tail on the side of long period. That suggests the attractor of this system has complex structure composed of at least three types of sub-attractors: a "Gamma attractor"-involved with several Poisson processes, a "deterministic attractor"-the residence time is deterministic, and a "stable attractor"-each pattern is stable. When the coupling strength was small, only the Gamma attractor was observed and switching behavior among patterns R, P I, and P A almost always via an asynchronous pattern named O. A conjecture is as follows: Internal/external noise exposes each pattern of R, P I, and P A coexisting around bifurcation points: That is observed as the Gamma attractor. As coupling strength increases, the deterministic attractor appears then followed by the stable attractor, always accompanied with the Gamma attractor. Switching behavior could be caused by regular existence of the Gamma attractor.

KW - Chaotic itinerancy

KW - Coupled oscillators

KW - Physarum polycephalum

KW - Slime mold

KW - Spatio-temporal pattern

KW - Switching

KW - Transition

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U2 - 10.1016/j.physd.2006.09.001

DO - 10.1016/j.physd.2006.09.001

M3 - Article

AN - SCOPUS:33750457359

SN - 0167-2789

VL - 223

SP - 180

EP - 188

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 2

ER -