Hopf bifurcation analysis of a reaction–diffusion Sel'kov system
作者： Wei Han , Zhenhua Bao
DOI: 10.1016/J.JMAA.2009.03.058
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摘要: Abstract A reaction–diffusion system known as the Sel'kov model subject to homogeneous Neumann boundary condition is investigated, where detailed Hopf bifurcation analysis performed. We not only show existence of spatially homogeneous/non-homogeneous periodic solutions system, but also derive conditions for determining direction and stability bifurcating solution.
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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
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
Rui Peng, Qualitative analysis of steady states to the Sel'kov model Journal of Differential Equations. ,vol. 241, pp. 386- 398 ,(2007) , 10.1016/J.JDE.2007.06.005
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
Mingxin Wang, Stability and Hopf bifurcation for a prey-predator model with prey-stage structure and diffusion. Bellman Prize in Mathematical Biosciences. ,vol. 212, pp. 149- 160 ,(2008) , 10.1016/J.MBS.2007.08.008
Rui Peng, Mingxin Wang, Ming Yang, Positive steady-state solutions of the Sel'kov model Mathematical and Computer Modelling. ,vol. 44, pp. 945- 951 ,(2006) , 10.1016/J.MCM.2006.03.001
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
Fengqi Yi, Junjie Wei, Junping Shi, None, Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system Journal of Differential Equations. ,vol. 246, pp. 1944- 1977 ,(2009) , 10.1016/J.JDE.2008.10.024
Bin Chen, Mingxin Wang, Qualitative analysis for a diffusive predator-prey model Computers & Mathematics With Applications. ,vol. 55, pp. 339- 355 ,(2008) , 10.1016/J.CAMWA.2007.03.020