Transitory behaviors in diffusively coupled nonlinear oscillators |
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Authors: | Tadokoro Satoru Yamaguti Yutaka Fujii Hiroshi Tsuda Ichiro |
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Institution: | (1) Laboratory of Computational Life Science, Research Institute of Electronic Science, Hokkaido University, Sapporo 060-0812, Japan;(2) Department of Information and Communication Sciences, Kyoto Sangyo University, Kyoto 603-8555, Japan;(3) Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan |
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Abstract: | We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly
interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings,
there appear various collective behaviors depending on the coupling strength, regardless of the number of oscillators. Among
others, we focus on an intermittent behavior consisting of the all-synchronized state, a weakly chaotic state and some sorts
of metachronal waves. Here, a metachronal wave means a wave with orderly phase shifts of oscillations. Such phase shifts are
produced by the dephasing interaction which produces the out-of-phase synchronized states in two coupled oscillators. We also
show that the abovementioned intermittent behavior can be interpreted as in-out intermittency where two saddles on an invariant
subspace, the all-synchronized state and one of the metachronal waves play an important role. |
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Keywords: | Diffusively coupled systems of oscillators Out-of-phase synchrony Metachronal waves In-out intermittency |
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