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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

## Abstract

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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## References

Shi, W. F. , 2007, “ An Analysis of Fractal and Chaotic Oscillation of Two Marine Generators Connected in Parallel,” J. Harbin Eng. Univ., 28(9), pp. 960–965.
Zhao, M. , Fan, Y. H. , and Xu, A. , 2007, “ Chaotic Character Analysis of Ship Power Load Time Series,” Seventh International Symposium on Test Measurement, Beijing, China, Aug. 5–8, pp. 6057–6059.
Zhao, M. , Fan, Y. H. , and Sun, H. , 2008, “ Chaos Local Forecasting of Electric Propulsion Ship Power Load on Multivariate Time Series,” J. Syst. Simul., 20, pp. 2797–2799.
Wang, X. Y. , Zhao, M. , and Fan, Y. H. , 2010, “ Ship Power Load Forecasting Based on Chaos Time Series Analysis Method,” J. Dalian Univ. Technol., 50(1), pp. 141–144.
Zhao, M. , Wang, S. H. , Liu, L. , and Zhao, Y. , 2009, “ Chaos Forecasting of Electric Propulsion Ship Power Load Based on Dead Weight Load Influence,” J. Syst. Simul., 21(18), pp. 5845–5848.
Liu, Y. , Guo, C. , Sun, J. B. , and Sun, C. Q. , 2009, “ Dynamic Process Simulation Research of Ship Electric Power System,” J. Syst. Simul., 21(9), pp. 2791–2795.
Chen, P. , Li, J. H. , and Lan, H. , 2011, “ Modeling and PSCAD Simulation Analysis on a Ship Power System,” Appl. Mech. Mater., 143–144, pp. 58–62.
Feng, X. Y. , Butler-Purry, K. L. , and Zourntos, T. , 2015, “ A Multi-Agent System Framework for Real-Time Electric Load Management in MVAC All-Electric Ship Power Systems,” IEEE Trans. Power Syst., 30(3), pp. 1327–1336.
Zhu, Z. Y. , Liu, W. T. , and Liang, S. Q. , 2010, “ Chaos Analysis for Ship Power System,” J. Jiangsu Univ. Sci. Technol.(Nat. Sci. Ed.), 24(2), pp. 164–168.
Zhu, Z. Y. , and Chen, R. P. , 2013, “ The Biggest Collapse Path of Brittleness of Ship Power System Based on Chaos Particle Swarm Optimization,” J. Wuhan Univ. Technol., 35(3), pp. 68–72.
Zhu, Z. Y. , Liu, W. T. , and Cai, L. Y. , 2010, “ Control of Warship Power System Chaos Based on Adaptive Backstepping,” Ship Build. China, 51(2), pp. 169–174.
Huang, M. L. , 2013, “ Chaos Control of Diesel-Generator Set Operating in Parallel,” J. Nav. Univ. Eng., 25(2), pp. 5–13.
Shen, N. J. , Liu, H. D. , Pang, Y. , Yu, H. N. , and Lan, H. , 2014, “ Research on Ship Shaft Power Generation System Based on BDFG and Its Grid-Connected Control Strategy,” Appl. Mech. Mater., 448–453, pp. 2830–2833.
Wang, C. , and Wang, G. , 2015, “ Research and Simulation on Nonlinear Control of Ship Power System,” Ship Sci. Technol., 37(1), pp. 161–164.
Naseradinmousavi, P. , Segala, D. B. , and Nataraj, C. , 2016, “ Chaotic and Hyperchaotic Dynamics of Smart Valves System Subject to a Sudden Contraction,” ASME J. Comput. Nonlinear Dyn., 11(5), p. 051025.
Naseradinmousavi, P. , Bagheri, M. , Krstic, C. , and Nataraj, C. , 2016, “Coupled Chaotic and Hyperchaotic Dynamics of Actuated Butterfly Valves Operating in Series,” ASME Paper No. DSCC2016-9601.
Wiggins, S. , 1990, Introduction to Applied Non-Linear Dynamical Systems and Chaos, Springer, New York.
Nayfeh, A. H. , and Balachandran, B. , 1995, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, Wiley, New York.
Bikdash, M. , Balachandran, B. , and Nayfeh, A. H. , 1994, “ Melnikov Analysis for a Ship With a General Roll-Damping Model,” Nonlinear Dyn., 6(1), pp. 101–124.
Zhang, W. N. , and Zhang, W. D. , 1999, “ Chaotic Oscillation of a Nonlinear Power System,” Appl. Math. Mech., 20(10), pp. 1175–1183.
Zhu, Z. Y. , Cai, L. Y. , and Liu, W. T. , 2008, “ Computation of Chaotic Oscillation Parameter in Electrical Power System Based on Melnikov Method,” Proc. CSU-EPSA, 20(3), pp. 41–45.
Wang, X. D. , Chen, Y. S. , Han, G. , and Song, C. Q. , 2015, “ Nonlinear Dynamic Analysis of a Single-Machine Infinite-Bus Power System,” Appl. Math. Modell., 39(10–11), pp. 2951–2961.
Siewe Siewe, M. , Moukam Kakmeni, F. F. , Tchawoua, C. , and Woafo, P. , 2006, “ Nonlinear Response and Suppression of Chaos by Weak Harmonic Perturbation Inside a Triple Well ϕ6-Rayleigh Oscillator Combined to Parametric Excitations,” ASME J. Comput. Nonlinear Dyn., 1(3), pp. 196–204.
Nana Nbendjo, B. R. , 2012, “ Nonlinear Dynamics of Inverted Pendulum Driven by Airflow,” ASME J. Comput. Nonlinear Dyn., 7(1), p. 011013.
Li, J. B. , and Chen, F. J. , 2012, Chaos, Melnikov Method and Its New Development, Science Press, Beijing, China.
Chen, L. J. , and Li, J. B. , 2004, “ Chaotic Behavior and Subharmonic Bifurcations for a Rotating Pendulum Equation,” Int. J. Bifurcation Chaos, 14(10), pp. 3477–3488.
Bonnin, M. , 2008, “ Harmonic Balance, Melnikov Method and Nonlinear Oscillators Under Resonant Perturbation,” Int. J. Circuit Theory Appl., 36(3), pp. 247–274.
Bonnin, M. , 2013, “ Horseshoe Chaos and Subharmonic Orbits in the Nanoelectromechanical Casimir Nonlinear Oscillator,” Int. J. Circuit Theory Appl., 41(6), pp. 583–602.

## Figures

Fig. 1

The phase portrait of system (5)

Fig. 2

The critical curves of b¯ for chaos

Fig. 3

The critical curves of c¯ for chaos

Fig. 4

The critical curves of a¯ for chaos

Fig. 9

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

Fig. 8

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

Fig. 7

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

Fig. 6

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

Fig. 5

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

Fig. 10

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

Fig. 11

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

Fig. 12

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

Fig. 13

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

Fig. 14

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

Fig. 15

The bifurcation diagram for b ∈ [1.5, 1.9]

## Errata

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