Bifurcation and chaos of a non-autonomous rotational machine systems

Simulation Modelling Practice and Theory

Volumn 16, Issue 10, 2008, Pages 1588-1605

  Zhang, Jian Gang ^a   Yu, Jian Ning ^a   Chu, Yan Dong ^a   Li, Xian Feng ^a   Chang, Ying Xiang ^a  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

Centrifugal governor; Chaos; Hopf bifurcation; Lyapunov exponents; Periodic motion; Phase locking; Poincar sections

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; ELECTRIC ENERGY STORAGE; EQUATIONS OF MOTION; FLYWHEELS; GOVERNORS; INTEGRATION; LINEAR EQUATIONS; LYAPUNOV METHODS; SYSTEM STABILITY; TELECOMMUNICATION NETWORKS; WHEELS;

CENTRIFUGAL GOVERNOR; CHAOS; LYAPUNOV EXPONENTS; PERIODIC MOTION; PHASE LOCKING;

HOPF BIFURCATION;

EID: 55249088590     PISSN: 1569190X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.simpat.2007.09.009     Document Type: Article

References (41)

1. Merta H. Characteristic time series and operation region of the system of two tank reactors (CSTR) with variable division of recirculation stream. Chaos, Solitons & Fractals 27 (2006) 279-285
2. Merta H. Chaotic dynamics of a cascade of plugow tubular reactors (PFTRs) with division of recirculating stream. Chaos, Solitons & Fractals 23 (2005) 1211-1219
3. Stachowiak T., and Okada T. A numerical analysis of chaos in the double pendulum. Chaos, Solitons & Fractals 29 (2006) 417-422
4. Kahraman A., and Blankenship G.W. Experiments on non-linear dynamic behavior of an oscillator with clearance and periodically time-varying parameters. Journal of Applied Mechanics 64 (1997) 217-226
5. Chen L.-Q., and Liu Y.-Z. A modified exact linearization control for chaotic oscillators. Nonlinear Dynamics 20 4 (2001) 309-317
6. Gakkhar S., and Singh B. Complex dynamic behavior in a food web consisting of two preys and a predator. Chaos, Solitons & Fractals 24 24 (2005) 789-801
7. Silver E.A. Changing the givens in modeling inventory problems: the example of just-in-time systems. International Journal of Production Economics 26 (1992) 347-351
8. Minegishi S., and Thiel D. System dynamics modeling and simulation of a particular food supply chain. Simulation Practice and Theory 8 (2000) 321-339
9. Dejonckheere J., Disney S.M., Lambrecht M.R., and Towill D.R. The impact of information enrichment on the Bullwhip effect in supply chains: a control theoretic approach. European Journal of Operations Research 153 3 (2004) 727-750
10. Gakkhar S., and Singh B. Dynamics of modified Leslie-Gower-type prey-predator model with seasonally varying parameters. Chaos, Solitons & Fractals 27 (2006) 1239-1255
11. Chu F., and Holmes R. Efficient computation on nonlinear responses of a rotating assembly incorporating the squeeze-film damper. Computer Methods in Applied Mechanics and Engineering 164 (1998) 363-373
12. Choi S.K., and Noah S.T. Response and stability analysis of piecewise-linear oscillators under multi-forcing frequencies. Nonlinear Dynamics 3 (1992) 105-121
13. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos (1990), Springer-Verlag, New York
14. Ge Z.M., and Lee J.K. Chaos synchronization and parameter identification for gyroscope system. Applied Mathematics and Computation 163 (2005) 667-682
15. Mahamoud G.M., Mohamed A.A., and Aly S.A. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 292 (2001) 193-206
16. Chen L.-Q., and Liu Y.-Z. A modified exact linearization control for chaotic oscillators. Nonlinear Dynamics 20 4 (2001) 309-317
17. Ge Z.M., and Leu W.Y. Anti-control of chaos of two-degrees-of-freedom loudspeaker system and chaos synchronization of different order systems. Chaos, Solitons & Fractals 20 (2004) 503-521
18. Chen H.-K., and Ge Z.-M. Bifurcations and chaos of a two-degree-of-freedom dissipative gyroscope. Chaos, Solitons & Fractals 24 (2005) 125-136
19. Chen G., and Ueta T. Yet another chaotic attractor. International Journal of Bifurcation Chaos 9 (1999) 1465-1466
20. Ge Z.-M., and Chen Y.-S. Adaptive synchronization of unidirectional and mutual coupled chaotic systems. Chaos, Solitons & Fractals 26 (2005) 881-888
21. Guckenheimer J., and Holmes P.J. Nonlinear Oscillations of Dynamical Systems and Bifurcations of Vector Fields (1983), Springer, New York
22. Beltrami E. Mathematics for Dynamic Modeling (1987), Academic Press lnc., Boston
23. J.P. Jensen, A.F. Kristensen, S.C. Sorenson, N. Houbak, E. Hendricks, Mean value modelling of a small turbocharged diesel engine, SAE Technical Paper No. 910070, 1991.
24. Sotomayor J., Mello L.F., and Braga D.C. Stability and Hopf bifurcation in the Watt governor system. Communications in Applied Numerical Methods 13 4 (2006) 1-17
25. Maxwell J.C. On governors. Proceedings of the Royal Society of London 16 (1868) 220-283
26. Vyshnegradskii I.A. Sur la théeorie générale des régulateurs. Comptes Rendus de l Academie des Sciences Paris 83 (1876) 18-321
27. Pontryagin L.S. Ordinary Differential Equations (1962), Addison-Wesley Publishing Company Inc., Reading
28. Denny M. Watt steam governor stability. European Journal of Physics 23 (2002) 339-351
29. Sotomayor J., Mello L.F., and Braga D.C. Stability and Hopf bifurcation in the Watt governor system. Communications in Applied Nonlinear Analysis 13 4 (2006) 1-17
30. Al-Humadi A., and Kazarinoff N.D. Hopf bifurcation in the Watt steam engine. Bulletin of the Institute of Mathematical Application 21 (1985) 133-136
31. Zhujun J., Chang Y., and Guanrong C. Complex dynamics in a permanent-magnet synchronous motor model. Chaos, Solitons & Fractals 22 (2004) 831-848
32. Ge Z.-M., and Lee C.-I. Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring. Journal of Sound and Vibration 262 (2003) 845-864
33. Ge Z.-M., and Lee C.-I. Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor. Journal of Sound and Vibration 282 (2005) 635-648
34. Zhang J.-G., Chu Y.-D., Chang Y.-X., and Li X.-F. Hopf bifurcation and chaos control for a type of centrifugal governor. Journal of Vibration and Shock 25 6 (2006) 127-131
35. Zhang J.-G., Li X.-F., Chu Y.-D., and Chang Y.-X. Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system. Chaos, Solitons & Fractals (2007) 10.1016/j.chaos.2007.06.131
36. Chu Y.D., Zhang J.G., Li X.F., Chang Y.X., and Luo G.W. Chaos and chaos synchronization for a non-autonomous rotational machine systems. Nonlinear Analysis: Real World Applications (2007) 10.1016/j.nonrwa.2007.03.009
37. Oseledec V.I. A multiplicative ergodic theorem. Transactions of the Moscow Mathematical Society 19 (1968) 197-231
38. Wolf A., Swift J., Swinney H., and Vastano J. Determining Lyapunov exponents from a time series. Physica D 16 (1985) 285-317
39. Kaplan J.L., and Yorke J.A. Chaotic behavior of multidimensional difference equations. In: Peitgen H.O., and Walther H.O. (Eds). Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics vol. 730 (1979), Springer-Verlag, Berlin 204-227
40. Yan-Zhu L., and Li-Qun C. Nonlinear Vibrations (2001), Higher Education Press, Beijing
41. Horn R.A., and Johnson C.R. Topics in Matrix Analysis (1991), Cambridge University Press, Cambridge