Bifurcation and stability analysis of nonlinear waves in Dn symmetric delay differential systems

Journal of Differential Equations

Volumn 232, Issue 2, 2007, Pages 521-543

  Peng, Mingshu ^a  

^a BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

Dn equivariant bifurcations; Delay; Lie group action; Multistability; Spatio temporal behavior

Indexed keywords

EID: 33750634090     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.09.010     Document Type: Article

References (16)

1. Buono P.-L., and Bélair J. Restrictions and unfolding of double Hopf bifurcation in functional differential equations. J. Differential Equations 189 1 (2003) 234-266
2. Campbell S.A., Yuan Y., and Bungay S. Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling. Nonlinearity 18 (2005) 2827-2846
3. S.A. Campbell, I. Ncube, J. Wu, Multistability and stable asynchronous periodic oscillation in a multiple-delayed neural system, preprint
4. Diekmann O., van Gils S.A., Verduyn S.M., and Walther H.-O. Delay Equations: Functional, Complex, and Nonlinear Analysis. Appl. Math. Sci. vol. 110 (1995), Springer-Verlag, New York
5. Faria T., Huang W.Z., and Wu J. Smoothness of center manifolds for maps and formal adjoints for semilinear FDEs in general Banach spaces. SIAM J. Math. Anal. 34 1 (2002) 173-203
6. Golubitsky M., Stewart I., and Schaeffer D.G. Singularities and Groups in Bifurcation Theory, vol. II. Appl. Math. Sci. vol. 69 (1988), Springer-Verlag, New York
7. Guo S. Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay. Nonlinearity 18 5 (2005) 2391-2407
8. Guo S., and Huang L. Hopf bifurcating periodic orbits in a ring of neurons with delays. Phys. D 183 (2003) 19-44
9. Hassard B.D., Kazarinoff N.D., and Wan Y.H. Theory and Applications of Hopf Bifurcation. London Math. Soc. Lecture Note Ser. vol. 41 (1981), Cambridge Univ. Press, Cambridge
10. Huang L., and Wu J. Nonlinear waves in networks of neurons with delayed feedback: pattern formation and continuation. SIAM J. Math. Anal. 34 4 (2003) 836-860
11. Peng M., and Yuan Y. Synchronization and desynchronization in a delayed discrete neural network. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 17 3 (2007)
12. 4 symmetry, Chaos Solitons Fractals, in press
13. M. Peng, Y. Yuan, Stability, symmetry-breaking bifurcation and chaos in discrete delayed models, in preparation
14. Wu J. Symmetric functional-differential equations and neural networks with memory. Trans. Amer. Math. Soc. 350 (1998) 4799-4838
15. Wu J., Faria T., and Huang Y.S. Synchronization and stable phase-locking in a network of neurons with memory. Math. Comput. Modelling 30 (1999) 117-138
16. Y. Yuan, J. Wei, Multiple bifurcation analysis in a neural network model with delay, Internat. J. Bifur. Chaos Appl. Sci. Engrg., in press