An algorithm to control chaotic behavior in one-dimensional maps

Computers and Mathematics with Applications

Volumn 31, Issue 6, 1996, Pages 13-22

  Gora P ^a   Boyarsky, A ^a  

^a Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

Control of dynamical system; Markov maps; Probability density function absolutely continuous invariant measure

Indexed keywords

EID: 0002515326     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00002-8     Document Type: Article

References (14)

1. T. Shinbrot, E. Ott, C. Grebogi and J.A. Yorke, Using chaos to direct orbits to targets in systems describable by a one-dimensional map, Physical Review A 45 (6), 4165-4168 (March 1992).
2. T. Shinbrot, E. Ott, C. Grebogi and J.A. Yorke, Using chaos to direct trajectories to targets, Physical Review Letters 65 (26), 3215-3218 (December 1990).
3. D. Auerbach, C. Grebogi, E. Ott and J.A. Yorke, Controlling chaos in high dimensional systems, Physical Review Letters 69, (24), 3497-3482 (December 1992).
4. E. Ott, C. Grebogi and J.A. Yorke, Controlling chaotic dynamical systems, In Chaos: Soviet-American Perspectives on Nonlinear Science (Edited by P.K. Campbell), pp. 153-172, American Institute of Physics, New York, (1990) ; Phys. Rev. Lett. 64, 1196 (1990).
5. E. Ott, C. Grebogi and J.A. Yorke, Controlling chaotic dynamical systems, In Chaos: Soviet-American Perspectives on Nonlinear Science (Edited by P.K. Campbell), pp. 153-172, American Institute of Physics, New York, (1990) ; Phys. Rev. Lett. 64, 1196 (1990).
6. T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M. Spano and J.A. Yorke, Using the sensitive dependence of chaos (the "Butterfly Effect") to direct trajectories in an experimental chaotic system, Physical Review Letters 68 (19), 2863-2866 (May 1992).
7. F.J. Romeiras, C. Grebogi, E. Ott and W.P. Dayawansa, Controlling chaotic dynamical systems, Physica D 58, 165-192 (1992).
8. Y.-C. Lai and C. Grebogi, Synchronization of chaotic trajectories using control, Physical Review E 47 (4), 2357-2360 (April 1993).
9. Y.-C. Lai, M. Ding and C. Grebogi, Controlling Hamiltonian chaos, Physical Review E 47 (1), 86-92 (January 1993).
10. T. Shinbrot, C. Grebogi, E. Ott and J.A. Yorke, Using chaos to target stationary states of flow, Physics Letters A 169, 349-354 (1992).
11. E.J. Kostelich, C. Grebogi, E. Ott and J.A. Yorke, Higher dimensional targeting, Physical Review E 47 (1), 305-310 (January 1993).
12. T. Shinbrot, C. Grebogi, E. Ott and J.A. Yorke, Using small perturbations to control chaos, Review article, Nature 363, 411-417 (June 1993).
13. P. Góra and A. Boyarsky, A matrix solution to the inverse Perron-Probenius problem, Proc. Amer. Math. Soc. 118, 409-414 (1993).
14. P. Góra and A. Boyarsky, Compactness of invariant densities for families of expanding monotonic transformations, Can. Journal Math. 41, 855-869 (1989).