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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

Annihilation of two interfaces in a hybrid system

Pages: 857 - 869, Volume 8, Issue 5, October 2015      doi:10.3934/dcdss.2015.8.857

 
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Shin-Ichiro Ei - Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita ward, Sapporo, 060-0810, Japan (email)
Kei Nishi - Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita ward, Sapporo, 060-0810, Japan (email)
Yasumasa Nishiura - WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan (email)
Takashi Teramoto - Asahikawa Medical University, 2-1-1-1, Midorigaoka-higashi, Asahikawa 078-8510, Japan (email)

Abstract: We consider the mixed ODE-PDE system called a hybrid system, in which the two interfaces interact with each other through a continuous medium and their equations of motion are derived in a weak interaction framework. We study the bifurcation property of the resulting hybrid system and construct an unstable standing pulse solution, which plays the role of a separator for dynamic transition from standing breather to annihilation behavior between two interfaces.

Keywords:  Dynamical system, reaction-diffusion, interface equation, annihilation dynamics.
Mathematics Subject Classification:  Primary: 37L10, 35K57; Secondary: 37G10.

Received: January 2014;      Revised: June 2014;      Available Online: July 2015.

 References