Control of chaos in excitable physiological systems: A geometric analysis

Chaos

Volumn 7, Issue 4, 1997, Pages 544-549

  Christini, David J ^a   Collins, James J ^a  

^a Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000175956     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166279     Document Type: Article

References (33)

1. M. C. Mackey and L. Glass, Science 197, 287 (1977).
2. L. Glass and M. C. Mackey, Ann. (N.Y.) Acad. Sci. 316, 214 (1979).
3. M. C. Mackey and J. G. Milton, Ann. (N.Y.) Acad. Sci. 504, 16 (1987).
4. M. R. Guevara, L. Glass, and A. Shrier, Science 214, 1350 (1981).
5. J. Bélair, L. Glass, U. an der Heiden, and J. Milton, Chaos 5, 1 (1995).
6. L. Glass, Phys. Today 49(8), 40 (1996).
7. N. S. Nise, Control Systems Engineering (The Benjamin/Cummings Publishing Company, Inc., Redwood City, California, 1992), p. 630.
8. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
9. W. L. Ditto, S. N. Rauseo, and M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
10. E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
11. R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
12. V. Petrov, V. Gáspár, J. Masere, and K. Showalter, Nature (London) 361, 240 (1993).
13. B. Hübinger, R. Doerner, W. Martienssen, W. Herdering, R. Pitka, and U. Dressler, Phys. Rev. E 50, 932 (1994).
14. R. Jan de Korte, J. C. Schouten, and C. M. van den Bleek, Phys. Rev. E 52, 3358 (1995).
15. D. J. Christini, J. J. Collins, and P. S. Linsay, Phys. Rev. E 54, 4824 (1996).
16. A. Garfinkel, M. L. Spano, W. L. Ditto, and J. N. Weiss, Science 257, 1230 (1992).
17. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, Nature (London) 370, 615 (1994).
18. D. J. Christini and J. J. Collins, Phys. Rev. Lett. 75, 2782 (1995).
19. L. Glass and W. Zeng, Int. J. Bifurcation Chaos 4, 1061 (1994).
20. M. E. Brandt and G. Chen, Int. J. Bifurcation Chaos 6, 715 (1996).
21. D. J. Christini and J. J. Collins, Phys. Rev. E 53, R49 (1996).
22. K. Hall, D. J. Christini, M. Tremblay, J. J. Collins, L. Glass, and J. Billette, Phys. Rev. Lett. 78, 4518 (1997).
23. Two control techniques (Refs. 19 and 20) that also directly perturb the controlled system variable have been developed for the control of cardiac chaos modeled by a one-dimensional map system. These techniques are only applicable to one-dimensional systems, in contrast to the PPF control technique which is applicable to higher dimensional systems.
24. Recently, an OGY-type control technique has been used to control a pathological cardiac rhythm in a numerical model (Ref. 21) and in an in vitro rabbit heart preparation (Ref. 22).
25. For PPF control, it is important to draw a distinction between the suprathreshold stimulus and the perturbation. The stimulus is clearly a large perturbation to the action-potential dynamics (as noted in Ref. 19); however, the PPF perturbation (δx) can be quite small.
26. With demand pacing, stimuli are used to prevent x from exceeding some pre-determined value. See: M. R. Neumann, in Medical Instrumentation Application and Design, 2nd ed., edited by J. G. Webster (Houghton Mifflin, Boston, 1992), pp. 699-700.
27. D. Pierson and F. Moss, Phys. Rev. Lett. 75, 2124 (1995).
28. X. Pei and F. Moss, Nature (London) 379, 618 (1996).
29. P. So, E. Ott, S. J. Schiff, D. T. Kaplan, T. Sauer, and C. Grebogi, Phys. Rev. Lett. 76, 4705 (1996).
30. D. T. Kaplan, Physica D 73, 38 (1994).
31. T. Sauer, Fields Inst. Commun. 11, 63 (1997).
32. n .
33. UPOs appear as unstable periodic fixed points on a first-return map.