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Sufficient conditions for wave instability in three-component reaction–diffusion systems

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Hata,  Shigefumi
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Mikhailov,  Alexander S.
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Citation

Hata, S., Nakao, H., & Mikhailov, A. S. (2014). Sufficient conditions for wave instability in three-component reaction–diffusion systems. Progress of Theoretical and Experimental Physics, 2014(1): 013A01. doi:10.1093/ptep/ptt102.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0015-791D-B
Abstract
Sufficient conditions for wave instability in general three-component reaction–diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to determine whether wave instability can be observed as the mobility of one of the species is gradually increased. It is found that the instability can also occur if one of the three species does not diffuse. Our results provide a useful criterion for searching wave instabilities in reaction–diffusion systems of various origins.