Skip to main content
SpringerLink
Log in

Diagnosing multistability by offset boosting

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

Abstract

An offset-boosting-based approach is developed for multistability identification in dynamical systems, where nonbifurcation operations are used for diagnosing multistability. Compared with the amplitude control method, the proposed approach has three distinguished features: easiness to introduce a parameter for offset boosting; reliability for finding coexisting attractors from arbitrary initial conditions; vigilance for identifying coexisting symmetric pairs of attractors. The proposed approach can identify coexisting hidden or self-excited attractors.

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. Arecchi, F.T., Meucci, R., Puccioni, G., Tredicce, J.: Experimental evidence of subharmonic bifurcations, multistability and turbulence in a Q-switched gas laser. Phys. Rev. Lett. 49, 1217 (1982)

    Article  Google Scholar 

  2. Foss, J., Longtin, A., Mensour, B., Milton, J.: Multistability and delayed recurrent loops. Phys. Rev. Lett. 76, 708 (1996)

    Article  Google Scholar 

  3. Laurent, M., Kellershohn, N.: Multistability: a major means of differentiation and evolution in biological systems. Trends Biochem. Sci. 24, 418–422 (1999)

    Article  Google Scholar 

  4. Joshi, A., Xiao, M.: Optical multistability in three-level atoms inside an optical ring cavity. Phys. Rev. Lett. 91, 143904 (2003)

    Article  Google Scholar 

  5. Ozbudak, E.M., Thattai, M., Lim, H.N., Shraiman, B.I., Oudenaarden, A.V.: Multistability in the lactose utilization network of Escherichia coli. Nature 427, 737–740 (2004)

    Article  Google Scholar 

  6. Lai, Q., Chen, S.: Research on a new 3D autonomous chaotic system with coexisting attractors. Optik 127, 3000–3004 (2016)

    Article  Google Scholar 

  7. Lai, Q., Chen, S.: Generating multiple chaotic attractors from Sprott B system. Int. J. Bifurc. Chaos 26, 1650177 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  8. Xu, Q., Lin, Y., Bao, B., Chen, M.: Multiple attractors in a non-ideal active voltage-controlled memristor based Chua’s circuit. Chaos Soliton Fract. 83, 186–200 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kengne, J., Njitacke, Z.T., Fotsin, H.B.: Dynamical analysis of a simple autonomous jerk system with multiple attractors. Nonlinear Dyn. 83, 751–765 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kengne, J., Njitacke, Z.T., Nguomkam, Negou A., Fouodji, Tsostop M., Fotsin, H.B.: Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit. Int. J. Bifurc. Chaos 26, 1650081 (2016)

    Article  MATH  Google Scholar 

  11. Bao, B.C., Bao, H., Wang, N., Chen, M., Xu, Q.: Hidden extreme multistability in memristive hyperchaotic system. Chaos Solit Fractals 94, 102–111 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, M., Xu, Q., Lin, Y., Bao, B.C.: Multistability induced by two symmetric stable node-foci in modified canonical Chua’s circuit. Nonlinear Dyn. 87, 789–802 (2017)

    Article  Google Scholar 

  13. Bao, B., Li, Q., Wang, N., Xu, Q.: Multistability in Chua’s circuit with two stable node-foci. Chaos 26, 043111 (2016)

    Article  MathSciNet  Google Scholar 

  14. Li, C., Sprott, J.C.: Multistability in the Lorenz system: a broken butterfly. Int. J. Bifurc. Chaos. 24, 1450131 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sprott, J.C.: A dynamical system with a strange attractor and invariant tori. Phys. Lett. A 378, 1361–1363 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  16. Li, C., Hu, W., Sprott, J.C., Wang, X.: Multistability in symmetric chaotic systems. Eur. Phys. J. Spec. Top. 224, 1493–1506 (2015)

    Article  Google Scholar 

  17. Li, C., Sprott, J.C.: Coexisting hidden attractors in a 4-D simplified Lorenz system. Int. J. Bifurc. Chaos. 24, 1450034 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  18. Sprott, J.C.: Simplest chaotic flows with involutional symmetries. Int. J. Bifurc. Chaos 24, 1450009 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sprott, J.C., Xiong, A.: Classifying and quantifying basins of attraction. Chaos 25, 083101 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. Li, C., Sprott, J.C.: Amplitude control approach for chaotic signals. Nonlinear Dyn. 73, 1335–1341 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Li, C., Sprott, J.C., Yuan, Z., Li, H.: Constructing chaotic systems with total amplitude control. Int. J. Bifurc. Chaos 25, 1530025 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  22. Li, C., Sprott, J.C.: Finding coexisting attractors using amplitude control. Nonlinear Dyn. 78, 2059–2064 (2014)

    Article  MathSciNet  Google Scholar 

  23. Li, C., Sprott, J.C., Xing, H.: Crisis in amplitude control hides in multistability. Int. J. Bifurc. 26, 1650233-1-11 (2016)

    MATH  MathSciNet  Google Scholar 

  24. Li, C., Sprott, J.C., Xing, H.: Hypogenetic chaotic jerk flows. Phys. Lett. A 380, 1172–1177 (2016)

  25. Li, C., Sprott, J.C., Xing, H.: Constructing chaotic systems with conditional symmetry. Nonlinear Dyn. 87, 1351–1358 (2017)

  26. Li, C., Sprott, J.C.: Variable-boostable chaotic flows. Optik 127, 10389–10398 (2016)

    Article  Google Scholar 

  27. Sprott, J.C., Wang, X., Chen, G.: Coexistence of point, periodic and strange attractors. Int. J. Bifurc. Chaos 23, 1350093 (2013)

    Article  MathSciNet  Google Scholar 

  28. Leonov, G.A., Vagaitsev, V.I., Kuznetsov, N.V.: Localization of hidden Chua’s attractors. Phys. Lett. A. 375, 2230–2233 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  29. Jafari, S., Sprott, J.C., Nazarimehr, F.: Recent new examples of hidden attractors. Eur. Phys. J. Spec. Top. 224, 1469–1476 (2015)

    Article  Google Scholar 

  30. Wei, Z., Wang, R., Liu, A.: A new finding of the existence of hidden hyperchaotic attractors with no equilibria. Math. Comput. Simul. 100, 13–23 (2014)

    Article  MathSciNet  Google Scholar 

  31. Kapitaniak, T., Leonov, G.A.: Multistability: uncovering hidden attractors. Eur. Phys. J. Spec. Top. 224, 1405–1408 (2015)

    Article  Google Scholar 

  32. Dudkowski, D., Jafari, S., Kapitaniak, T., Kuznetsov, N.V., Leonovc, G.A., Prasad, A.: Hidden attractors in dynamical systems. Phys. Rep. 637, 1–50 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  33. Jiang, H., Liu, Y., Wei, Z., Zhang, L.: Hidden chaotic attractors in a class of two-dimensional maps. Nonlinear Dyn. 85, 2719–2727 (2016)

    Article  MathSciNet  Google Scholar 

  34. Munmuangsaen, B., Srisuchinwong, B.: A new five-term simple chaotic attractor. Phys. Lett. A 373, 4038–4043 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  35. van der Schrier, G., Maas, L.R.M.: The diffusionless Lorenz equations; Shil’nikov bifurcations and reduction to an explicit map. Phys. Nonlinear Phenom. 141, 19–36 (2000)

    Article  MATH  Google Scholar 

  36. Li, C., Sprott, J.C.: Multistability in a butterfly flow. Int. J. Bifurc. Chaos 23, 1350199 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  37. Liu, J., Liu, S., Sprott, J.C.: Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters. Nonlinear Dyn. 83, 1109–1121 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  38. Liu, J., Liu, S., Yuan, C.: Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters. Nonlinear Dyn. 9, 1035–1047 (2015)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported financially by the Startup Foundation for Introducing Talent of NUIST (Grant No.: 2016205), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.: 16KJB120004), the Advantage Discipline “Information and Communication Engineering” of Jiangsu Province, and a Project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Author information

Authors and Affiliations

  1. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chunbiao Li

  2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chunbiao Li

  3. Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, China

    Xiong Wang

  4. Department of Electronic Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong

    Guanrong Chen

Authors
  1. Chunbiao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guanrong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunbiao Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Wang, X. & Chen, G. Diagnosing multistability by offset boosting. Nonlinear Dyn 90, 1335–1341 (2017). https://doi.org/10.1007/s11071-017-3729-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3729-1

Keywords

Search

Navigation