BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY

Shangjiang Guo; Jie Li

doi:10.11948/2015057

2015 Volume 5 Issue 4

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Shangjiang Guo, Jie Li. BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 751-766. doi: 10.11948/2015057

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Shangjiang Guo, Jie Li. BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 751-766. doi: 10.11948/2015057

BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY

Shangjiang Guo¹,
Jie Li²

1 College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People's Republic of China;
2 School of Physics and Electronics, Hunan University, Changsha, Hunan 410082, People's Republic of China

Fund Project:

Abstract

Abstract

In this paper we survey the topic of bifurcation theory of functional differential equations. We begin with a brief discussion of the position of bifurcation and functional differential equations in dynamical systems. We follow with a survey of the state of the art on the bifurcation theory of functional differential equations, including results on Hopf bifurcation, center manifold theory, normal form theory, Lyapunov-Schmidt reduction, and degree theory.
- Hopf bifurcation /
- center manifold theory /
- normal form theory /
- Lyapunov-Schmidt reduction /
- degree theory
MSC: 34K18;35K32

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References

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