2002 Fiscal Year Final Research Report Summary
Dynamics of oscillatory and excitable fields with nanlocal coupling
| Project/Area Number |
13831005
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Institution | Kyoto University |
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Principal Investigator |
KURAMATO Yoshiki Kyoto University, Graduate School of Sciences, 大学院・理学研究科, 教授 (40037247)
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| Project Period (FY) |
2001 – 2002
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| Keywords | reaction-diffusion / nanlecal / oscillator / reduction / rotating spiral wave / soft-made turbulence / spatio-temporal chans / complex Ginzburg-Landan |
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| Research Abstract |
In this research project, a variety of new types of pattern dynamics exhibited by self-oscillatory media with effective non-local coupling were studied theoretically. A specific 3-component reaction-diffusion model as well as its reduced form near the Hopf bifurcation were analyzed mathematically and numerically
1. Existence of rotating spiral waves without phase singularity was demonstrated. This occurs when a group of oscillators near the spiral core, which experience relatively weak internal field, fails to synchronize with this field. Our reaction-diffusion model and its reduction were confirmed to exhibit this behavior
2. Existence of soft-mode turbulence was confirmed. Soft-mode turbulence is a type of spatio-temporal chaos which arises when a spatially uniform state becomes Turing unstable under the condition that the system already breaks a certain continuous symmetry. A linear stability analysis for our reduced equation (non-locally coupled complex GL equation) was carried out, which revealed that the type of eigenvalue spectrum peculiar to soft-mode turbulence appear under suitable condition. Direct numerical simulation of the equation confirmed the occurrence of the expected turbulent behavior
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