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Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators.
We show that a wide class of uncoupled limit-cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study theExpand
Complex Ginzburg-Landau equation with nonlocal coupling.
  • Dan Tanaka, Y. Kuramoto
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and…
  • 26 August 2003
TLDR
Stability analysis of the reduced equation about the uniform oscillation revealed that new types of instability which can never arise in the ordinary complex Ginzburg-Landau equation are possible. Expand
Large-scale vortex lattice emerging from collectively moving microtubules
TLDR
This study reports experiments in which microtubules are propelled by surface-bound dyneins, providing evidence for the existence of previously unsuspected universality classes of collective motion phenomena. Expand
Chemical turbulence equivalent to Nikolavskii turbulence.
  • Dan Tanaka
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and…
  • 9 March 2004
We find evidence that a certain class of reaction-diffusion (RD) systems can exhibit chemical turbulence equivalent to Nikolaevskii turbulence. We study an extended complex Ginzburg-Landau (CGL)Expand
Critical exponents of Nikolaevskii turbulence.
  • Dan Tanaka
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and…
  • 3 December 2004
TLDR
It is argued that in some previous studies, parameter values for which this type of turbulence does not appear were mistakenly considered, and the spectrum becomes qualitatively indistinguishable from that of Kuramoto-Sivashinsky turbulence. Expand
General chemotactic model of oscillators.
  • Dan Tanaka
  • Physics, Medicine
  • Physical review letters
  • 28 September 2007
TLDR
A simpler model describing the phases and positions of the chemotactic elements by means of center-manifold and phase-reduction methods is derived and it is found that, despite its simplicity, the model obtained through this reduction exhibits a rich variety of patterns. Expand
Noise Induced Phase Synchronization of a General Class of Limit Cycle Oscillators(Oscillation, Chaos and Network Dynamics in Nonlinear Science)
We consider the effect of weak additive noise to a general class of limit cycle oscillators. Employing phase reduction method, the largest Lyapunov exponent of the noise driven oscillators are shownExpand
Arnold tongue of electrochemical nonlinear oscillators.
TLDR
Higher harmonics included in a limit cycle describing the isolated oscillator, dependence on the redox reaction, and hysteresis due to a bistability are discussed. Expand
Mechanism underlying the diverse collective behavior in the swarm oscillator model
Abstract The swarm oscillator model describes the long-time behavior of interacting chemotactic particles, and it shows numerous types of macroscopic patterns. However, the reason why so many kindsExpand
Dimensionality of clusters in a swarm oscillator model.
  • M. Iwasa, Dan Tanaka
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and…
  • 23 June 2010
TLDR
This work analytically finds the conditions of the appearance of patterns which oscillators form in the three-oscillator system and proves the validity of those conditions in applying to systems of more oscillators. Expand
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