Bifurcation control of two nonlinear models of cardiac activity

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 44, Issue 10, 1997, Pages 1031-1034

  Brandt, Michael E ^a   Chen, Guanrong ^a  

^a UNIVERSITY OF TEXAS MEDICAL SCHOOL   (United States)

Author keywords

Bifurcation; Cardiology; Chaos; Control; Dynamical system

Indexed keywords

BIFURCATION (MATHEMATICS); CARDIOLOGY; CHAOS THEORY; FEEDBACK CONTROL; MATHEMATICAL MODELS;

OTT GREBOGI YORKE (OGY) METHOD;

NONLINEAR CONTROL SYSTEMS;

EID: 0031258280     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.633897     Document Type: Article

References (13)

1. L. Glass, "Dynamics of cardiac arrhythmias," Phys. Today, pp. 40-45, Aug. 1996.
2. A. Garfinkel, M. L. Spano, W. L. Ditto, and J. N. Weiss, "Controlling cardiac chaos," Sci., vol. 257, pp. 1230-1235, 1992.
3. E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos," Phy. Rev. Lett., vol. 64, pp. 1196-1199, 1990.
4. W. L. Ditto, "Applications of chaos in biology and medicine," in Chaos and the Changing Nature of Science and Medicine: An Introduction, D. E. Herbert, Ed. New York: AIP Press, 1996, pp. 175-201.
5. L. Glass and W. Zeng, "Bifurcations in flat-topped maps and the control of cardiac chaos," Int. J. Bifurc. Chaos, vol. 4, pp. 1061-1067, 1994.
6. M. E. Brandt and G. Chen, "Feedback control of a quadratic map model of cardiac chaos," Int. J. Bifurc. Chaos, vol. 6, pp. 715-723, 1996.
7. M. E. Brandt, A. Ademoglu, D. Lai, and G. Chen, "Autoregressive self-tuning feedback control of the Henon map," Phys. Rev. E, vol. 54, pp. 6201-6206, 1996.
8. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992, p. 130.
9. M. E. Brandt and G. Chen, "Controlling the dynamical behavior of a circle map model of the human heart," Biol. Cybern., vol. 74, pp. 1-8, 1996.
10. M. Courtemanche, L. Glass, J. Belair, D. Scagliotti, and D. Gordon,"A circle map in a human heart," Physica D, vol. 40, pp. 299-310, 1989.
11. W. Z. Zeng, M. Courtemanche, L. Sehn, A. Shrier, and L. Glass, "Theoretical computation of phase locking in embryonic atrial heart cell aggregates," J. Theor. Biol., vol. 145, pp. 225-244, 1990.
12. Y. He, R. Chi, and N. He, "Lyapunov exponents of the circle map in human hearts," Phys. Lett. A, vol. 170, pp. 29-32, 1992.
13. K. Pyragas, "Continuous control of chaos by self-controlling feedback," Phys. Lett. A, vol. 170, pp. 421-428, 1992.