Biomedical subjects

Kei-Ichi Ueda

Publications and source records attributed to Kei-Ichi Ueda.

4 recordsLinked to original sources

PubMed2005

Scattering of traveling spots in dissipative systems.

One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there occur many collisions among them and its scattering manner is crucial to predict whether periodic structure is realized or not. We focus on the colliding dynamics of traveling spots arising in a three-component system and study how the transition of scattering dynamics is brought about. It has been clarified that hidden unstable patterns called "scattors" and their stable and unstable manifolds direct the traffic flow of orbits before and after collisions. The collision process in general can be decomposed into several steps and each step is controlled by such a scattor, in other words, a network among scattors forms the backbone for scattering dynamics. A variety of input-output relations comes from the complexity of the network as well as high Morse indices of the scattor. The change of transition manners is caused by the switching of the network from one structure to another, and such a change is caused by the singularities of scattors. We illustrate a typical example of the change of transition caused by the destabilization of the scattor. A new instability of the scattor brings a new destination for the orbit resulting in a new input-output relation, for instance, Hopf instability for the scattor of peanut type brings an annihilation.

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PubMed2004

Phase-dependent output of scattering process for traveling breathers.

Scattering 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.

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PubMed2003

Scattering and separators in dissipative systems.

Scattering of particlelike patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision in the one-dimensional(1D) space where traveling pulses interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of steady or time-periodic solutions called separators and their stable and unstable manifolds direct the traffic flow of orbits. Such separators are, in general, highly unstable even in the 1D case which causes a variety of input-output relations through the scattering process. We illustrate the ubiquity of separators by using the Gray-Scott model and a three-component reaction diffusion model arising in gas-discharge phenomena.

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PubMed2003

Dynamic transitions through scattors in dissipative systems.

Scattering of particle-like patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision where traveling pulses or spots interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of unstable steady or time-periodic solutions called scattors and their stable and unstable manifolds direct the traffic flow of orbits. Such scattors are in general highly unstable even in the one-dimensional case which causes a variety of input-output relations through the scattering process. We illustrate the ubiquity of scattors by using the complex Ginzburg-Landau equation, the Gray-Scott model, and a three-component reaction diffusion model arising in gas-discharge phenomena.

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