Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system

Chaos, Solitons and Fractals

Volumn 39, Issue 5, 2009, Pages 2150-2168

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

^a LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CENTRIFUGATION; CHAOS THEORY; EQUATIONS OF MOTION; FLYWHEELS; GOVERNORS; HOPF BIFURCATION; LYAPUNOV FUNCTIONS; NONLINEAR EQUATIONS; WHEELS;

BIFURCATION DIAGRAM; CONTROLLING CHAOS; DYNAMICAL BEHAVIORS; LAGRANGIAN EQUATIONS; LONG-TERM BEHAVIOR; LYAPUNOV DIMENSION; NONLINEAR BEHAVIOR; PERIODIC AND CHAOTIC MOTIONS;

LYAPUNOV METHODS;

EID: 64049103801     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.06.131     Document Type: Article

References (40)

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 plug flow 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. Gakkhar S., and Singh B. Complex dynamic behavior in a food web consisting of two preys and a predator. Chaos, Solitons & Fractals 24 (2005) 789-801
5. Gakkhar S., and Naji R.K. Chaos in seasonally perturbed ratio-dependent prey-predator system. Chaos, Solitons & Fractals 15 (2003) 107-118
6. Gakkhar S., and Naji R.K. Order and chaos in a food web consisting of a predator and two independent preys. Commun Nonlinear Sci Numer Simul 10 (2005) 105-120
7. Gakkhar S., and Naji R.K. Existence of chaos in two-prey, one-predator system. Chaos, Solitons & Fractals 17 (2003) 639-649
8. 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
9. Ott E., Grebogi N., and Yorke J. Controlling chaos. Phys Rev Lett 64 11 (1990) 1196-1199
10. Agiza H.N. Controlling chaos for the dynamical system of coupled dynamics. Chaos, Solitons & Fractals 13 (2002) 341-352
11. Pyragas K. Phys Lett A 170 (1992) 421
12. Lai Y., and Grebogi C. Phys Rev E 47 (1993) 2357
13. Ahmed E., Misiery A.E., and Agiza H.N. On controlling chaos in an inflation-unemployment dynamical system. Chaos, Solitons & Fractals 10 9 (1999) 1567-1570
14. Ahmed E., Agiza H.N., and Hassan S.Z. On modelling advertisement in Cournot duopoly. Chaos, Solitons & Fractals 10 7 (1999) 1179-1184
15. Yagasaki K., and Uozumi T. Controlling chaos using nonlinear approximations and delay coordinate embedding. Phys Lett A 247 (1998) 129-139
16. Ramesh M., and Narayanan S. Chaos control by nonfeedback methods in the presence of noise. Chaos, Solitons & Fractals 10 9 (1999) 1473-1489
17. Yassen M.T. Chaos control of Chen chaotic dynamical system. Chaos, Solitons & Fractals 15 (2003) 271-283
18. Lynch S., and Steele A.L. Controlling chaos in nonlinear optical resonators. Chaos, Solitons & Fractals 11 (2000) 721-728
19. 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
20. Koumboulis F.N., and Mertzios B.G. Feedback controlling against chaos. Chaos, Solitons & Fractals 11 (2000) 351-358
21. Kapitaniak T. Continuous control and synchronization in chaotic systems. Chaos, Solitons & Fractals 6 (1995) 237-244
22. Harb A.M., and Jabbar N.A. Controlling Hopf bifurcation and chaos in a small power system. Chaos, Solitons & Fractals 18 (2003) 1055-1063
23. Liu S., and Chen G. Nonlinear feedback-controlled generalized synchronization of spatial chaos. Chaos, Solitons & Fractals 22 (2004) 35-46
24. Wang X., and Tian L. Tracing control of chaos for the coupled dynamos dynamical system. Chaos, Solitons & Fractals 21 4 (2004) 193-200
25. Yu Y., and Zhang S. Controlling uncertain system using back stepping design. Chaos, Solitons & Fractals 15 (2003) 897-902
26. Jackson E.A., and Grosu I. An open-plus-closed-loop (OPCL) control of complex dynamic systems. Physica D 85 (1995) 1-9
27. Chen L.Q., and Liu Y.Z. The modified open-plus-closed-loop control of chaos in nonlinear oscillations. Phys Lett A 245 (1998) 87-90
28. Chen L.Q. An open-plus-closed-loop control for discrete chaos and hyperchaos. Phys Lett A 281 (2001) 327-333
29. Grosu I. Robust synchronization. Phys Rev E 56 (1997) 3709-3712
30. Chen L.Q., and Liu Y.Z. An open-plus-closed-loop approach to synchronization of chaotic and hyperchaotic maps. Int J Bifurcat Chaos 12 (2002) 1219-1225
31. Chen L.Q., and Liu Y.Z. Parametric open-plus-closed-loop control of chaos in continuous dynamical systems. Acta Mech Solida Sinica 10 (1997) 316-321
32. Chen L.Q., and Liu Y.Z. A parametric open-plus-closed-loop approach to control chaos in nonlinear oscillations. Phys Lett A 262 (1999) 350-357
33. Chen L.Q. The parametric open-plus-closed-loop control of chaotic maps and its robustness. Chaos, Solitons & Fractals 21 (2004) 113-118
34. Beltrami E. Mathematics for dynamic modeling (1987), Academic Press Inc., Boston p. 162-8
35. 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. J Sound Vib 262 (2003) 845-864
36. Wolf A., Swift J., Swinney H., and Vastano J. Determining Lyapunov exponents from a time series. Physica D 16 (1985) 285-317
37. 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
38. Yan-zhu L., and Li-qun C. Nonlinear vibrations (2001), Higher Education Press, Beijing
39. Ogata K. Modern control engineering (1990), Prentice-Hall
40. Jackson E.A., and Grosu I. Int J Bifurcat Chaos 5 (1995) 1767