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Nonlinear Dynamics

, Volume 89, Issue 3, pp 1889–1903 | Cite as

Impulsive stabilization of chaos in fractional-order systems

  • Marius-F. DancaEmail author
  • Michal Fečkan
  • Guanrong Chen
Original Paper

Abstract

This paper considers a class of nonlinear impulsive Caputo differential equations of fractional order, which models chaotic systems. Computer-assisted proof of chaos suppression by stabilizing the unstable system equilibria is provided. A nonexistence result of periodic solutions is presented, and the commensurate fractional-order Lorenz system is simulated for illustration.

Keywords

Impulsive Caputo differential equation of fractional order Adams–Bashforth–Moulton method Chaos stabilization 

Notes

Acknowledgements

The authors thank to Professor Julien Clinton Sprott for interesting discussions related to the energy approach. M.-F. Danca is supported by Tehnic B SRL. M. Fečkan is supported in part by the Slovak Research and Development Agency under the Contract No. APVV-14-0378 and by the Slovak Grant Agency VEGA Nos. 2/0153/16 and 1/0078/17. G. Chen is supported by the Hong Kong Research Grants Council under the GRF Grant CityU 11234916.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceAvram Iancu University of Cluj-NapocaCluj-NapocaRomania
  2. 2.Romanian Institute of Science and TechnologyCluj-NapocaRomania
  3. 3.Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and InformaticsComenius University in BratislavaBratislavaSlovak Republic
  4. 4.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovak Republic
  5. 5.Department of Electronic EngineeringCity University of Hong KongHong KongChina

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