Advertisement

Nonlinear Dynamics

, Volume 81, Issue 3, pp 1381–1392 | Cite as

A spherical chaotic system

  • Guoyuan Qi
  • Guanrong Chen
Original Paper

Abstract

This paper proposes a spherical chaotic system by appropriately combining a celestial conservative system with a dissipative chaotic system. The spherical system spins around its axis chaotically while revolving along an elliptical orbit. The spherical system takes on rich dynamics: having spherical four-wing chaotic attractors, spherical ring-like chaotic attractors, spherical periodic orbits and spherical sink orbits, as the dissipative sub-system is perturbed through parameter variations.

Keywords

Dissipative chaotic system  Celestial conservative system Spherical chaotic attractor 

Notes

Acknowledgments

This work was supported in part by the Incentive Funding of National Research Foundation of South Africa (IFR150130113354) and by the Hong Kong Research Grants Council under the GRF Grant CityU112014.

References

  1. 1.
    Cang, S., Qi, G., Chen, Z.: A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dyn. 59, 515–527 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Coca, A.E., Tost, G.O., Zhao, L.: Characterizing chaotic melodies in automatic music composition. Chaos 20, 033125 (2010)CrossRefGoogle Scholar
  3. 3.
    Guo, L., Hu, M., Xu, Z., Hu, A.: Synchronization and chaos control by quorum sensing mechanism. Nonlinear Dyn. 73, 1253–1269 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lü, J., Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12, 659–661 (2002)CrossRefGoogle Scholar
  5. 5.
    Qi, G., Du, S., Chen, G., Chen, Z., Yuan, Z.: On a 4-dimensional chaotic system. Chaos Solitons Fractals 23, 1671–1682 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Qi, G., Chen, G., Li, S., Zhang, Y.: Four-wing attractors: from pseudo to real. Int. J. Bifurc. Chaos 16, 859–885 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Qi, G., Chen, G., van Wyk, M.A., van Wyk, B.J., Zhang, Y.: A four-wing chaotic attractor generated from a new 3-D quadratic chaotic system. Chaos Solitons Fractals 38, 705–721 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dadras, S., Reza, M.H., Qi, G.: Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos. Nonlinear Dyn. 62, 391–405 (2010)CrossRefGoogle Scholar
  9. 9.
    Cang, S., Qi, G., Chen, Z.: A four-wing-hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dyn. 46, 263–270 (2010)MathSciNetGoogle Scholar
  10. 10.
    Qi, G., Wang, Z., Guo, Y.: Generation of an eight-wing chaotic attractor from Qi 3-D four-wing chaotic system. Int. J. Bifurc. Chaos 22, 1250287 1-9 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Parker, B.R.: Chaos in the Cosmos: the Stunning Complexity of the Universe. Plenum Press, NY (1996)CrossRefGoogle Scholar
  12. 12.
    Wisdom, J.: Meteorites may follow a chaotic route to earth. Nature, 315, 731–733 (1985)Google Scholar
  13. 13.
    Rangarajan, G.: Kolmogorov-Arnold-Moser theorem-Can planetary motion be stable? Reson. J. Sci. Educ. 3, 43–53 (1998)Google Scholar
  14. 14.
    Buchler, R., Regev, O.: Chaos in stellar variability. In: Krasner, S. (ed.) The Ubiquity of Chaos, vol. 218. American Association for the Advancement of Science, NY (1990)Google Scholar
  15. 15.
    Caranicolas, N.D., Innanen, K.A.: Chaos in a galaxy model with nucleus and bulge components. Astron. J. 102, 1343 (1991)CrossRefGoogle Scholar
  16. 16.
    Hasan, H., Normman, C.: Chaotic orbits in barred galaxies with central mass concentrations. Astropkysictd J. 361, 69 (1990)CrossRefGoogle Scholar
  17. 17.
    Chandrasekhar, S.: The two-centre problem in general relativity: the scattering of radiation of two extreme r. n. black holes. Proc. R. Soc. Lond. A 421, 227 (1989)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Contoupolos, G.F.: Periodic orbits and chaos around two black holes. Proc. R. Soc. Lond. A 431, 183 (1990)CrossRefGoogle Scholar
  19. 19.
    Morbidelli, A.: Modern Celestial Mechanics Aspect of Solar System Dynamics in the Solar System. Taylor & Francis, London (2002)Google Scholar
  20. 20.
    Shen, C., Yu, S., Lü, J., Chen, G.: Designing hyperchaotic systems with any desired number of positive Lyapunov exponents via a simple model. IEEE Trans. Circuits Syst. I Regul. Pap. 61, 2380–2389 (2014)Google Scholar
  21. 21.
    Shen, C., Yu, S., Lü, J., Chen, G.: A systematic methodology for constructing hyperchaotic systems with multiple positive Lyapunov exponents and circuit implementation. IEEE Trans. Circuits Syst. I Regul. Pap. 61, 854–864 (2014)Google Scholar
  22. 22.
    Qi, G., van Wyk, M.A., van Wyk, B.J., Chen, G.: On a new hyperchaotic system. Phys. Lett. A. 372/2, 124–136 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.College of Electrical Engineering and AutomationTianjin Polytechnic UniversityTianjinPeople’s Republic of China
  2. 2.Department of Electrical and Mining EngineeringUniversity of South AfricaFloridaSouth Africa
  3. 3.Department of Electronic EngineeringCity University of Hong KongKowloonPeople’s Republic of China

Personalised recommendations