1991 Fiscal Year Final Research Report Summary
Self-organization of the excitable field in a reaction-diffusion system
| Project/Area Number |
01460041
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Ochanomizu University |
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Principal Investigator |
OHTA Takao Ochanomizu University, Physics, Professor, 理学部, 教授 (50127990)
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| Project Period (FY) |
1989 – 1991
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| Keywords | Non equilibrium open system / reaction-diffusion equation / singular perturbation / phase-amplitude equation / propagating pulse / dynamical multistability |
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| Research Abstract |
We have studied the dynamcs and the pattern formation in an excitable reaction-diffusion system so called Bonhoeffer-van der Pol(BVP)type equation. This set of equations has been used for modeling pulse propagation along the nerve axiom and Belousov-Zhabotinsky reaction. Furthermore, it admits not only the time-dependent solutions but also a spatially periodic steady solution where excited domains constitute a periodic lattice. It is also known that an excited domain undergoes a breathing motion by changing the parameter.
One of the most characteristic features of nonequilibrium open systems is the existence of temporal order and of spatially localized pattern. Both are originated from the absence of any Lyapounov functionals. Here I shall summarize the results obtained emphasizing the conceptual aspects.
A spatially periodic structure in a reaction-diffusion system has been interpreted by the diffusional instability. However, we have shown that BVP equation in a particular limit reduces to a variational system. The Lyapounov functional which contains both a short range and a long range intemdons is found to be essentially the same as the one for equilibrium mesophases such as block copolymer melts and smectic liquid crystals. Furthermore, the reduced system is closely related to the model equation for pattern formation in visual cortex. These are important properties of BVP equation unrecognized previously.
The other result that I would like to stress is the role of dynamical multistability far from equilibrium. We have shown that BVP equation exhibits various solutions which can coexist. For instance, An enphase and an anti-phase oscillations occur in the breathing motion of excited domains. We have also analyzed the coexistence region of a propagating pulse and a motionless domain. We expect that these multistabilitis are relevant to information transportation and self-organization in biological system. However further investigation is left for a future study.
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