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Journal of Applied Mathematics
Volume 2015, Article ID 657307, 12 pages
http://dx.doi.org/10.1155/2015/657307
Research Article

Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition

Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 14 May 2015; Accepted 12 July 2015

Academic Editor: Alain Miranville

Copyright © 2015 Cun-Hua Zhang and Xiang-Ping Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Theory of Bifurcations of Dynamical Systems on a Plane, Israel Program for Scientific Translations, Jerusalem, Israel, 1971.
  2. J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977. View at MathSciNet
  3. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, UK, 1981. View at MathSciNet
  4. H. Kielhófer, Bifurcation Theory: An Introduction with Applications to PDEs, vol. 156 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2004.
  5. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, Springer, New York, NY, USA, 1998. View at MathSciNet
  6. J.-H. Wu, Theory and Applications of Partial Functional Differential Equations, Springer, New York, NY, USA, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  7. F. Yi, J. Wei, and J. Shi, “Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system,” Journal of Differential Equations, vol. 246, no. 5, pp. 1944–1977, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. L.-J. Yang and X.-W. Zeng, “Stability of singular Hopf bifurcations,” Journal of Differential Equations, vol. 206, no. 1, pp. 30–54, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Y. Jin, J. P. Shi, J. J. Wei, and F. Q. Yi, “Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions,” Rocky Mountain Journal of Mathematics, vol. 43, no. 5, pp. 1637–1674, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. S. G. Ruan, “Diffusion-driven instability in the Gierer-Meinhardt model of morphogenesis,” Natural Resource Modeling, vol. 11, no. 2, pp. 131–142, 1998. View at Google Scholar · View at MathSciNet
  11. F. Yi, J. Wei, and J. Shi, “Diffusion-driven instability and bifurcation in the Lengyel-Epstein system,” Nonlinear Analysis: Real World Applications, vol. 9, no. 3, pp. 1038–1051, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. F. Q. Yi, J. J. Wei, and J. P. Shi, “Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system,” Applied Mathematics Letters, vol. 22, no. 1, pp. 52–55, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus