Turing structures and stability for the 1-D Lengyel–Epstein system
作者： Meihua Wei , Jianhua Wu , Gaihui Guo
DOI: 10.1007/S10910-012-0037-3
关键词:
摘要: This paper continues the analysis on Lengyel–Epstein reaction- diffusion system of chlorite-iodide-malonic acid-starch (CIMA) reaction for rich Turing structures. The steady state structures, especially double bifurcation one, and their stability multiplicity are studied by use Lyapunov–Schmidt reduction technique singularity theory. Numerical simulations presented to support our theoretical studies. results show that richer stationary patterns heavily rely both size reactor effective rate in CIMA reaction.
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sci-hub.se 参考文章(22)
Chemical waves and patterns Kluwer Academic Publishers. ,(1995) , 10.1007/978-94-011-1156-0
Wei-Ming Ni, Moxun Tang, Turing patterns in the Lengyel-Epstein system for the CIMA reaction Transactions of the American Mathematical Society. ,vol. 357, pp. 3953- 3969 ,(2005) , 10.1090/S0002-9947-05-04010-9
Martin Golubitsky, Ian Stewart, David G. Schaeffer, Singularities and groups in bifurcation theory Springer Science+Business Media. ,(1985) , 10.1007/978-1-4612-4574-2
Alan Mathison Turing, The Chemical Basis of Morphogenesis Philosophical Transactions of the Royal Society B. ,vol. 237, pp. 37- 72 ,(1952) , 10.1098/RSTB.1952.0012
Fengqi Yi, Junjie Wei, Junping Shi, Diffusion-driven instability and bifurcation in the Lengyel–Epstein system Nonlinear Analysis: Real World Applications. ,vol. 9, pp. 1038- 1051 ,(2008) , 10.1016/J.NONRWA.2007.02.005
Jaeduck Jang, Wei-Ming Ni, Moxun Tang, Global Bifurcation and Structure of Turing Patterns in the 1-D Lengyel–Epstein Model Journal of Dynamics and Differential Equations. ,vol. 16, pp. 297- 320 ,(2004) , 10.1007/S10884-004-2782-X
Jiayin Jin, Junping Shi, Junjie Wei, Fengqi Yi, Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of Cima chemical reactions Rocky Mountain Journal of Mathematics. ,vol. 43, pp. 1637- 1674 ,(2013) , 10.1216/RMJ-2013-43-5-1637
T. Nozakura, S. Ikeuchi, Formation of dissipative structures in galaxies The Astrophysical Journal. ,vol. 279, pp. 40- 52 ,(1984) , 10.1086/161863
Fengqi Yi, Junjie Wei, Junping Shi, Global asymptotical behavior of the Lengyel–Epstein reaction–diffusion system☆ Applied Mathematics Letters. ,vol. 22, pp. 52- 55 ,(2009) , 10.1016/J.AML.2008.02.003
Joel Smoller, Shock Waves and Reaction-Diffusion Equations ,(1983)