PMID: 15244921Jul 13, 2004Paper

Phase-dependent output of scattering process for traveling breathers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Takashi TeramotoYasumasa Nishiura

Abstract

Scattering process between one-dimensional traveling breathers (TBs), i.e., oscillatory traveling pulses, for the complex Ginzburg-Landau equation (CGLE) with external forcing and a three-component activator-substrate-inhibitor model are studied. The input-output relation depends in general on the phase of two TBs at collision point, which makes a contrast to the case for the steady traveling pulses. A hidden unstable solution called the scattor plays a crucial role to understand the scattering dynamics. Stable and unstable manifolds of the scattor direct the traffic flows of the scattering process. A transition point of the input-output relation in a parameter space such as from preservation to annihilation corresponds to when the orbit crosses the stable manifold of the scattor. The phase dependency of input-output relation comes from the fact that the profiles at collision point make a loop parametrized by the phase and it traverses the stable manifold of the scattor. A global bifurcation viewpoint is quite useful not only to understand how TBs emerge but also to detect scattors. It turns out that the scattor for the CGLE (respectively the three-component system) becomes an unstable time-periodic (respectively stationary) so...Continue Reading

References

Nov 15, 1991·Physical Review. a·P Kolodner
Sep 10, 1990·Physical Review Letters·P CoulletJ Lajzerowicz
Aug 10, 1992·Physical Review Letters·M BärG Ertl
Dec 5, 1994·Physical Review Letters·K Krischer, A Mikhailov
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yasumasa NishiuraKei-Ichi Ueda
Aug 30, 2003·Chaos·Yasumasa NishiuraKei-Ichi Ueda

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Citations

Oct 18, 2005·Biological cybernetics·Akane OhganeTatsuyuki Ohtsuki
Oct 2, 2007·Chaos·Yasumasa NishiuraKei-Ichi Ueda
Jan 7, 2006·Chaos·Yasumasa NishiuraKei-Ichi Ueda
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrzej L Kawczyński, Bartłomiej Legawiec
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xiaohui YuanYasumasa Nishiura
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kunishige Ohgane, Kei-Ichi Ueda
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yoji Kawamura
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takashi TeramotoYasumasa Nishiura
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kei-Ichi UedaToshiyuki Nakagaki

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