A nested sequence of transitions for collision dynamics in dissipative systems
by
Masaaki Yadome
Kei-Ichi Ueda
Takashi Teramoto
Masaharu Nagayama
Yasumasa Nishiura
Vol. 3 No. 4 (2008) P.585~P.601
ABSTRACT
We study the dynamics of head-on collisions of traveling pulses for a three-component reaction diffusion system. A variety of outputs with large deformation such
as annihilation, repulsion, and fusion are observed after collision, however it remains open for a long time that what kind of mathematical structure controls the input-output relation at collision point. A series of works [18, 19, 20, 24] clarify some aspect of scattering dynamics that a network of unstable patterns called $\it scattors$ forms
a backbone of the traffic control of input-output relations. Namely the unstable manifolds of those scattors constitute a network and complicated deformation processes
and their transitions are controlled by rewiring those connections depending on parameters. In this article, by employing a three-component reaction diffusion system, we numerically show that there occurs a nested
sequence of outputs among annihilation,
repulsion, and fusion as parameters are varied in an appropriate way. It turns out that there exists a time-periodic unstable
solution that plays a role of scattor
and two heteroclinic connections are detected between the unstable periodic solution and other unstable stationary scattors which are
responsible for the nested output of periodic type.
KEYWORDS
Reaction-diffusion systems, pattern formation, pulse dynamics, bifurcation
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 37M05, 37M20, 65P30
MILESTONES
Received: 2008-08-12
Revised :
Accepted: 2008-08-12
Download Full Content