TY - JOUR
T1 - Phase-dependent output of scattering process for traveling breathers
AU - Teramoto, Takashi
AU - Ueda, Kei Ichi
AU - Nishiura, Yasumasa
PY - 2004
Y1 - 2004
N2 - 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) solution.
AB - 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) solution.
UR - http://www.scopus.com/inward/record.url?scp=85036294796&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.69.056224
DO - 10.1103/PhysRevE.69.056224
M3 - 学術論文
C2 - 15244921
AN - SCOPUS:85036294796
SN - 1063-651X
VL - 69
SP - 8
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 5
ER -