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Research Papers

Subharmonic Bifurcations and Chaotic Dynamics for a Class of Ship Power System

[+] Author and Article Information
Liangqiang Zhou

Department of Mathematics,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: zlqrex@sina.com

Fangqi Chen

Professor
Department of Mathematics,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: fangqichen@nuaa.edu.cn

1Corresponding authors.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 13, 2017; final manuscript received January 9, 2018; published online February 1, 2018. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 13(3), 031011 (Feb 01, 2018) (9 pages) Paper No: CND-17-1265; doi: 10.1115/1.4039060 History: Received June 13, 2017; Revised January 09, 2018

Subharmonic bifurcations and chaotic dynamics are investigated both analytically and numerically for a class of ship power system. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and nonchaotic regions are obtained. The chaotic feature on the system parameters is discussed in detail. It is shown that there exist chaotic bands for this system. The conditions for subharmonic bifurcations with O type or R type are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations with O type, and it also can be chaotically excited through infinite subharmonic bifurcations with R type. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.

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Figures

Grahic Jump Location
Fig. 1

The phase portrait of system (5)

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Fig. 2

The critical curves of b¯ for chaos

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Fig. 3

The critical curves of c¯ for chaos

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Fig. 4

The critical curves of a¯ for chaos

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Fig. 5

The phase portraits of system (4) with b = 1.8

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Fig. 6

The time history curve of x for system (4) with b = 1.8

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Fig. 7

The time history curve of y for system (4) with b = 1.8

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Fig. 8

The Poincaré sections for system (4) with b = 1.8

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Fig. 9

The Lyapunov exponent spectrum for system (4) with b = 1.8

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Fig. 10

The phase portraits of system (4) with b = 1.6

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Fig. 11

The time history curve of x for system (4) with b = 1.6

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Fig. 12

The time history curve of y for system (4) with b = 1.6

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Fig. 13

The Poincaré sections for system (4) with b = 1.6

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Fig. 14

The Lyapunov exponent spectrum for system (4) with b = 1.6

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Fig. 15

The bifurcation diagram for b ∈ [1.5, 1.9]

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