Global asymptotical behavior of the Lengyel–Epstein reaction–diffusion system☆

作者: Fengqi Yi , Junjie Wei , Junping Shi

DOI: 10.1016/J.AML.2008.02.003

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摘要: Abstract The Lengyel–Epstein reaction–diffusion system of the CIMA reaction is revisited. We construct a Lyapunov function to show that constant equilibrium solution globally asymptotically stable when feeding rate iodide small. also for small spatial domains, all solutions eventually converge spatially homogeneous and time-periodic solution.

参考文章(11)
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
Sze-Bi Hsu, A SURVEY OF CONSTRUCTING LYAPUNOV FUNCTIONS FOR MATHEMATICAL MODELS IN POPULATION BIOLOGY Taiwanese Journal of Mathematics. ,vol. 9, pp. 151- 173 ,(2005) , 10.11650/TWJM/1500407791
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
Edward Conway, David Hoff, Joel Smoller, Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations SIAM Journal on Applied Mathematics. ,vol. 35, pp. 1- 16 ,(1978) , 10.1137/0135001
P. de Mottoni, F. Rothe, Convergence to Homogeneous Equilibrium State for Generalized Volterra–Lotka Systems with Diffusion Siam Journal on Applied Mathematics. ,vol. 37, pp. 648- 663 ,(1979) , 10.1137/0137048
P. De Kepper, V. Castets, E. Dulos, J. Boissonade, Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction Physica D: Nonlinear Phenomena. ,vol. 49, pp. 161- 169 ,(1991) , 10.1016/0167-2789(91)90204-M
Arkady Rovinsky, Michael Menzinger, Interaction of Turing and Hopf bifurcations in chemical systems. Physical Review A. ,vol. 46, pp. 6315- 6322 ,(1992) , 10.1103/PHYSREVA.46.6315