2008 / December Volume 3 No.4
A nested sequence of transitions for collision dynamics in dissipative systems
| Published Date |
2008 / December
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|---|---|
| Title | A nested sequence of transitions for collision dynamics in dissipative systems |
| Author | |
| Keyword | |
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| Pagination | 585-601 |
| 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.
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| AMS Subject Classification |
37M05, 37M20, 65P30
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| Received |
2008-08-12
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| Accepted |
2008-08-12
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