Skip to main content
SpringerLink
Log in

Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Parameter identification is an important issue in nonlinear science and has received increasing interest in the recent years. In this paper, an oppositional backtracking search optimization algorithm is proposed to solve the parameter identification of hyperchaotic system. The backtracking search optimization algorithm provides a new alternative for population-based heuristic search. To increase the diversity of initial population and to accelerate the convergence speed, the opposition-based learning method is employed in the backtracking search optimization algorithm for population initialization as well as for generation jumping. Numerical simulations on several typical hyperchaotic systems are conducted to demonstrate the effectiveness and robustness of the proposed scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Mahmoud, G.M., Mahmoud, E.E., Ahmed, M.E.: On the hyperchaotic complex Lü system. Nonlinear Dyn. 58(4), 725–738 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Swathy, P.S., Thamilmaran, K.: Hyperchaos in SC-CNN based modified canonical Chua’s circuit. Nonlinear Dyn. 78(4), 2639–2650 (2014)

    Article  MathSciNet  Google Scholar 

  3. Mahmoud, G.M., Mahmoud, E.E., Arafa, A.A.: On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications. Phys. Scr. 87(5), 10 (2013)

    Article  Google Scholar 

  4. Betancourt-Mar, J.A., Mendez-Guerrero, V.A., Hernandez-Rodriguez, C., Nieto-Villar, J.M.: Theoretical models for chronotherapy: periodic perturbations in hyperchaos. Math. Biosci. Eng. 7(3), 553–560 (2010). doi:10.3934/mbe.2010.7.553

    Article  MATH  MathSciNet  Google Scholar 

  5. Matouk, A.E., Elsadany, A.A.: Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique. Appl. Math. Lett. 29, 30–35 (2014)

    Article  MathSciNet  Google Scholar 

  6. Effati, S., Nik, H.S., Jajarmi, A.: Hyperchaos control of the hyperchaotic Chen system by optimal control design. Nonlinear Dyn. 73(1–2), 499–508 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  7. Xi, H., Yu, S., Zhang, R., Xu, L.: Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems. Optik Int. J. Light Electron Opt. 125(9), 2036–2040 (2014)

    Article  Google Scholar 

  8. Gambino, G., Sciacca, V.: Intermittent and passivity based control strategies for a hyperchaotic system. Appl. Math. Comput. 221, 367–382 (2013)

    Article  MathSciNet  Google Scholar 

  9. Jawaada, W., Noorani, M.S.M., Mossa Al-sawalha, M.: Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances. Nonlinear Anal. Real World Appl. 13(5), 2403–2413 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lan, Y., Li, Q.: Chaos synchronization of a new hyperchaotic system. Appl. Math. Comput. 217(5), 2125–2132 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hegazi, A.S., Matouk, A.E.: Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system. Appl. Math. Lett. 24(11), 1938–1944 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chen, D.-Y., Shi, L., Chen, H.-T., Ma, X.-Y.: Analysis and control of a hyperchaotic system with only one nonlinear term. Nonlinear Dyn. 67(3), 1745–1752 (2012)

    Article  MathSciNet  Google Scholar 

  13. Ma, C., Wang, X.: Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals. Nonlinear Dyn. 70(1), 551–558 (2012)

    Article  MATH  Google Scholar 

  14. Mahmoud, E.E.: Dynamics and synchronization of new hyperchaotic complex Lorenz system. Math. Comput. Model. 55(7–8), 1951–1962 (2012)

  15. Mahmoud, E.E.: Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear systems. Math. Methods Appl. Sci. 37(3), 321–328 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mahmoud, G.M., Mahmoud, E.E.: Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems. Nonlinear Dyn. 61(1–2), 141–152 (2010)

    Article  MATH  Google Scholar 

  17. Mahmoud, G.M., Mahmoud, E.E.: Lag synchronization of hyperchaotic complex nonlinear systems. Nonlinear Dyn. 67(2), 1613–1622 (2012)

    Article  MATH  Google Scholar 

  18. Konnur, R.: Synchronization-based approach for estimating all model parameters of chaotic systems. Phys. Rev. E 67(2), 4 (2003)

    Article  Google Scholar 

  19. Li, N., Pan, W., Yan, L., Luo, B., Xu, M., Jiang, N., Tang, Y.: On joint identification of the feedback parameters for hyperchaotic systems: an optimization-based approach. Chaos Solitons Fractals 44(4–5), 198–207 (2011)

    Article  Google Scholar 

  20. Austin, F., Sun, W., Lu, X.: Estimation of unknown parameters and adaptive synchronization of hyperchaotic systems. Commun. Nonlinear Sci. Numer. Simul. 14(12), 4264–4272 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Feng, J., Chen, S., Wang, C.: Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification. Chaos Solitons Fractals 26(4), 1163–1169 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  22. Hu, M., Xu, Z., Zhang, R., Hu, A.: Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems. Phys. Lett. A 361(3), 231–237 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  23. Mahmoud, G.M., Mahmoud, E.E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlinear Dyn. 62(4), 875–882 (2010)

    Article  MATH  Google Scholar 

  24. Mahmoud, G.M., Mahmoud, E.E., Arafa, A.A.: Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method. Chin. Phys. B 22(6), 9 (2013)

    Article  Google Scholar 

  25. He, Q., Wang, L., Liu, B.: Parameter estimation for chaotic systems by particle swarm optimization. Chaos Solitons Fractals 34(2), 654–661 (2007)

    Article  MATH  Google Scholar 

  26. Peng, B., Liu, B., Zhang, F.-Y., Wang, L.: Differential evolution algorithm-based parameter estimation for chaotic systems. Chaos Solitons Fractals 39(5), 2110–2118 (2009)

    Article  Google Scholar 

  27. Sheng, Z., Wang, J., Zhou, S., Zhou, B.: Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm. Chaos 24(1), 013133 (2014)

  28. Lin, J., Xu, L.: Parameter estimation for chaotic systems based on hybrid biogeography-based optimization. Acta Phys. Sin. 62(3), 030505 (2013)

  29. Wang, L., Xu, Y.: An effective hybrid biogeography-based optimization algorithm for parameter estimation of chaotic systems. Expert Syst. Appl. 38(12), 15103–15109 (2012)

  30. Civicioglu, P.: Backtracking search optimization algorithm for numerical optimization problems. Appl. Math. Comput. 219(15), 8121–8144 (2013)

  31. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution. IEEE Trans. Evolut. Comput. 12(1), 64–79 (2008)

    Article  Google Scholar 

  32. Tizhoosh, H.R.: Opposition-based learning: A new scheme for machine intelligence. In: International Conference on Computational Intelligence for Modelling Control and Automation, Vienna, Austria, November 28–30 2005, pp. 695–701. IEEE.

  33. Wang, H., Wu, Z., Rahnamayan, S., Liu, Y., Ventresca, M.: Enhancing particle swarm optimization using generalized opposition-based learning. Inf. Sci. 181(20), 4699–4714 (2011)

    Article  MathSciNet  Google Scholar 

  34. Wang, J., Wu, Z., Wang, H.: Hybrid differential evolution algorithm with chaos and generalized opposition-based learning. Adv. Comput. Intell. 6382, 103–111 (2010)

    Google Scholar 

  35. Lin, J., Chen, C.: Parameter estimation of chaotic systems by an oppositional seeker optimization algorithm. Nonlinear Dyn. 76(1), 509–517 (2014)

    Article  Google Scholar 

  36. Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: Proceedings of the 2007 IEEE Swarm Intelligence Symposium, Honolulu, Hawaii, April 2007, pp. 120–127. Proceedings of the 2007 IEEE Swarm Intelligence Symposium.

  37. Particle Swarm Central: (2013). http://www.particleswarm.info/. Accessed June 2013

  38. Haeri, M., Dehghani, M.: Impulsive synchronization of Chen’s hyperchaotic system. Phys. Lett. A 356(3), 226–230 (2006)

    Article  MATH  Google Scholar 

  39. Rössler, O.E.: An equation for hyperchaos. Phys. Lett. A 71(2–3), 155–157 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  40. Li, Y., Liu, X., Chen, G., Liao, X.: A new hyperchaotic Lorenz-type system: generation, analysis, and implementation. Int. J. Circuit Theory Appl. 39(8), 865–879 (2011)

    Google Scholar 

Download references

Acknowledgments

This work is part of a project supported by Scientific Research Fund of Zhejiang Provincial Education Department under Grant No. Y201432261, the National Natural Science Foundation of China under Grant No. 51475410, and the National Natural Science Foundation of China under Grant No. 61403338. The author also would like to thank the anonymous reviewers for their valuable comments and suggestions.

Author information

Authors and Affiliations

  1. School of Information, Zhejiang University of Finance & Economics, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Jian Lin

Authors
  1. Jian Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, J. Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems. Nonlinear Dyn 80, 209–219 (2015). https://doi.org/10.1007/s11071-014-1861-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1861-8

Keywords

Search

Navigation