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Impulsive control of chaotic attractors in nonlinear chaotic systems

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Abstract

Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented. By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.

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References

  1. Ott E, Grebogi C, Yorke J A. Chaos controlling[J].Phys Rev Lett, 1990,64(11): 1196–1199.

    Article  MATH  MathSciNet  Google Scholar 

  2. Pecora L M, Carroll T L. On the control and synchronization of chaos[J].Phys Rev Lett, 1990,64, (7):821–827.

    Article  MATH  MathSciNet  Google Scholar 

  3. Ramirez Avila G M, Guisset J L, Deneubourg J L. Synchronization in light-controlled oscillators [J]Phys D 2003,182(4):254–273.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chin Yi Chee, XU Dao-lin. Control of the formation of projective synchronisation in lower-dimensional discrete-time systems[J].Phys Lett A, 2003,318(12):112–118.

    Article  MATH  MathSciNet  Google Scholar 

  5. Stojanovski T, Kocarev L, Parlitz U. Driving and synchronizing by chaotic impulses[J].Phys Rev E, 1996,54(2):2128–2131.

    Article  Google Scholar 

  6. ZHU Jian-dong, TIAN Yu-ping. Nonlinear recursive delayed feedback control for chaotic discrete-time systems[J].Phys Lett A, 2003,310(2):295–300.

    MathSciNet  Google Scholar 

  7. YAMG Tao, YANG Lin-bao, YANG Chun-mei. Impulsive synchronization of Lorenz systems[J].Phys Lett A, 1997,226(6):349–354.

    Article  Google Scholar 

  8. HU Hai-yan. Main control on mechanics chaotic systems[J].Mechanics development, 1996,26 (4):453–463. (in Chinese)

    Google Scholar 

  9. CHEN Li-qun, LIU Zeng-rong. Control of a hyper chaotic discrete system[J].Applied Mathematics and Mechanics (English Edition), 2001,22(7):741–746.

    Article  Google Scholar 

  10. MA Jun-hai, CHEN Yu-shu. Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I) [J].Applied Mathematics and Mechanics (English Edition), 2001,22(11):1240–1251.

    Article  MathSciNet  Google Scholar 

  11. MA Jun-hai, CHEN Yu-shu. Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II)[J].Applied Mathematics and Mechanics (English Edition), 2001,22(12):1375–1382.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Management School, Tianjin University, 300072, Tianjin, P.R. China

    Ma Jun-hai Professor, Doctor & Ren Biao

  2. Tianjin University of Finance and Economics, 300222, Tianjin, P. R. China

    Ma Jun-hai Professor, Doctor

  3. Department of Mechanics, Tianjin University, 300072, Tianjin, P. R. China

    Chen Yu-shu Professor, Doctor, Foreign Academician of Russian Academy of Sciences

Authors
  1. Ma Jun-hai Professor, Doctor
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  2. Ren Biao
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  3. Chen Yu-shu Professor, Doctor, Foreign Academician of Russian Academy of Sciences
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Additional information

Contributed by CHEN Yu-shu

Foundation item: the National Natural Science Foundation of China (19990150, 70271071)

Biographies: MA Jun-hai (1965≈); CHEN Yu-shu (1931≈)

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Jun-hai, M., Biao, R. & Yu-shu, C. Impulsive control of chaotic attractors in nonlinear chaotic systems. Appl Math Mech 25, 971–976 (2004). https://doi.org/10.1007/BF02438345

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  • DOI: https://doi.org/10.1007/BF02438345

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2000 Mathematics Subject Classification

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