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


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.

Reaction-diffusion systems, pattern formation, pulse dynamics, bifurcation

Primary: 37M05, 37M20, 65P30


Received: 2008-08-12
Revised :
Accepted: 2008-08-12

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