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Erschienen in:
2012 | OriginalPaper | Buchkapitel
2. Nonlinear Discrete Dynamical Systems
verfasst von : Albert C. J. Luo
Erschienen in: Regularity and Complexity in Dynamical Systems
Verlag: Springer New York
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Abstract
In this chapter, the basic concepts of nonlinear discrete systems will be presented. The local and global theory of stability and bifurcation for nonlinear discrete systems will be discussed. The stability switching and bifurcation on specific eigenvectors of the linearized system at fixed points under specific period will be presented. The higher singularity and stability for nonlinear discrete systems on the specific eigenvectors will be developed. A few special cases in the lower dimensional maps will be presented for a better understanding of the generalized theory. The route to chaos will be discussed briefly, and the intermittency phenomena relative to specific bifurcations will be presented. The normalization group theory for 2-D discrete systems will be presented via Duffing discrete systems.