Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 2, 1999, Pages 1646-1655

  Dhamala, Mukeshwar ^a   Lai, Ying Cheng ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL REACTIONS; COMPUTER SIMULATION; DYNAMICS; ECOLOGY; ELECTRIC POTENTIAL; ELECTRIC POWER SYSTEMS; EQUATIONS OF MOTION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

TRANSIENT CHAOS CONTROL; VOLTAGE COLLAPSE;

CHAOS THEORY;

EID: 0033074344     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.1646     Document Type: Article

References (43)

1. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982)
2. C. GrebogiE. OttJ. A. YorkePhysica D 7, 181 (1983).
3. H. Kantz and P. Grassberger, Physica D 17, 75 (1985).
4. G. H. Hsu, E. Ott, and C. Grebogi, Phys. Lett. A 127, 199 (1988).
5. T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990), Vol. 3; T. Tél, in STATPHYS 19, edited by Bai-lin Hao (World Scientific, Singapore, 1996).
6. E. Ott and T. Tél, Chaos 3, 417 (1993), focus issue on chaotic scattering, edited by E. Ott and T. Tél.
7. C. Jung and E. Ziemniak, J. Phys. A 25, 3929 (1992)
8. C. Jung, T. Tél, and E. Ziemniak, Chaos 3, 555 (1993)
9. E. Ziemniak, C. Jung, and T. Tél, Physica D 76, 123 (1994)
10. �.� Péntek, T. Tél, and Z. Toroczkai, J. Phys. A 28, 2191 (1995)
11. Á. PéntekT. TélZ. ToroczkaiFractals 3, 33 (1995)
12. Á. Péntek, Z. Toroczkai, T. Tél, C. Grebogi, and J. Yorke, Phys. Rev. E 51, 4076 (1995)
13. Phys. Rev. EZ. Neufeld and T. Tél, 57, 2832 (1998)
14. Z. Toroczkai, G. Károlyi, Á. Péntek, T. Tél, and C. Grebogi, Phys. Rev. Lett. 80, 500 (1998).
15. I. Dobson and H.-D. Chiang, Syst. Control Lett. 13, 253 (1989).
16. H. Wang, E. H. Abed, and A. M. A. Hamdan, in Proceedings of the 1992 American Control Conference (Chicago) (American Autom. Control Council, Evanston, IL, 1992), pp. 2084–2088
17. H. Wang and E. H. Abed, in Proceedings of NOLCOS’92: Nonlinear Control System Design Symposium, Bordeaux, France, edited by M. Fliess (Pergamon, Oxford, UK, 1992), pp. 283–288;H. Wang, Ph.D. thesis, University of Maryland, 1993.
18. K. McCann and P. Yodzis, Am. Nat. 144, 873 (1994).
19. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
20. T. Tél, J. Phys. A 24, L1359 (1991)
21. T. TélInt. J. Bifurcation Chaos Appl. Sci. Eng. 3, 757 (1993).
22. Y.-C. Lai and C. Grebogi, Phys. Rev. E 49, 1094 (1994)
23. Phys. Rev. EY.-C. Lai, T. Tél, and C. Grebogi, 48, 709 (1993);Y.-C. Lai, C. Grebogi, and T. Tél, in Towards the Harnessing of Chaos, edited by M. Yamaguti (Elsevier, Amsterdam, 1994).
24. I. Schwartz and I. Triandaf, Phys. Rev. Lett. 77, 4740 (1996).
25. T. Kapitaniak and J. Brindley, Phys. Lett. A 241, 41 (1998).
26. J. L. Hudson, O. E. Rössler, and H. Killory, Chem. Eng. Commun. 46, 158 (1986).
27. P. Parmananda and M. Eiswirth, Phys. Rev. E 54, R1036 (1996).
28. S. L. Pimm, The Balance of Nature (University of Chicago Press, Chicago, 1991).
29. R. May, Nature (London) 261, 459 (1976).
30. A. Hastings , Annu. Rev. Ecol. Syst. 24, 1 (1993).
31. R. May, Am. Math. Soc. Trans. 32, 291 (1995).
32. R. D. Holt and M. A. McPeek, Am. Nat. 148, 709 (1997).
33. A. Hastings and K. Higgins, Science 263, 1133 (1994).
34. K. Alligood, T. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, New York, 1997).
35. Y.-C. Lai, C. Grebogi, and J. A. Yorke, in Applied Chaos, edited by J. H. Kim and J. Stringer (Wiley, New York, 1992).
36. K. G. Szabó and T. Tél, Phys. Lett. A 196, 173 (1994)
37. K. G. Szabó, Y.-C. Lai, T. Tél, and C. Grebogi, Phys. Rev. Lett. 77, 3102 (1996).
38. The issue of sustaining a desirable chaotic state from an intermittent time series as a result of interior crisis was addressed by Y. Nagai and Y.-C. Lai, Phys. Rev. E 51, 3842 (1995). A method based on stabilizing a long target chaotic trajectory was also proposed in that work. The applicability of this method is, however, limited, as it may be difficult to find a long target chaotic trajectory and small control perturbations needed to be applied at each time step.
39. The concept of a “threshold population size” may provide a useful rule of thumb for manipulating the dynamics. Similar ideas have been used elsewhere in conservation theory [R. Gomulkiewicz and R. D. Holt, Evolution (Lawrence, Kans.) 49, 201 (1995)].
40. M. Ding, E. Ott, and C. Gebogi, Phys. Rev. E 50, 4228 (1994).
41. V. In, S. Mahan, W. L. Ditto, and M. L. Spano, Phys. Rev. Lett. 74, 4420 (1995)
42. V. In, M. Spano, J. Neff, W. L. Ditto, C. Daw, K. D. Edwards, and K. Nguyen, Chaos 7, 605 (1997).
43. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, Nature (London) 370, 615 (1994).