2024-03-28T18:41:04Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/54292022-11-17T02:08:08Zhdl_2115_20057hdl_2115_148Phase-dependent output of scattering process for traveling breathersTeramoto, TakashiUeda, Kei-IchiNishiura, Yasumasa413Scattering 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.American Physical SocietyJournal Articleapplication/pdfhttp://hdl.handle.net/2115/5429https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/5429/1/PRE69-5pdf.pdf1063-651XPhysical Review E690562242004-05-27enginfo:pmid/15244921info:doi/10.1103/PhysRevE.69.056224Copyright © 2004 American Physical Societypublisher