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Research Papers

Center Manifold of Fractional Dynamical System

[+] Author and Article Information
Li Ma

Department of Mathematics,
Shanghai University,
Shanghai 200444, China
e-mail: mali20062787@163.com

Changpin Li

Department of Mathematics,
Shanghai University,
Shanghai 200444, China
e-mail: lcp@shu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 26, 2015; final manuscript received July 19, 2015; published online August 26, 2015. Assoc. Editor: Gabor Stepan.

J. Comput. Nonlinear Dynam 11(2), 021010 (Aug 26, 2015) (6 pages) Paper No: CND-15-1078; doi: 10.1115/1.4031120 History: Received March 26, 2015; Revised July 19, 2015

Dimension reduction of dynamical system is a significant issue for technical applications, as regards both finite dimensional system and infinite dimensional systems emerging from either science or engineering. Center manifold method is one of the main reduction methods for ordinary differential systems (ODSs). Does there exists a similar method for fractional ODSs (FODSs)? In other words, does there exists a method for reducing the high-dimensional FODS into a lower-dimensional FODS? In this study, we establish a local fractional center manifold for a finite dimensional FODS. Several examples are given to illustrate the theoretical analysis.

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Figures

Grahic Jump Location
Fig. 1

Stability regions of the FODS (7)

Grahic Jump Location
Fig. 2

Fractional center manifold for system (25)

Grahic Jump Location
Fig. 3

The approximation of fractional center manifold for system (37)

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