Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 1111–1123 | Cite as

Dissipative chaos, Shilnikov chaos and bursting oscillations in a three-dimensional autonomous system: theory and electronic implementation

  • Sifeu Takougang Kingni
  • Lars Keuninckx
  • Paul Woafo
  • Guy Van der Sande
  • Jan Danckaert
Original Paper


A three-dimensional autonomous chaotic system is presented and physically implemented. Some basic dynamical properties and behaviors of this system are described in terms of symmetry, dissipative system, equilibria, eigenvalue structures, bifurcations, and phase portraits. By tuning the parameters, the system displays chaotic attractors of different shapes. For specific parameters, the system exhibits periodic and chaotic bursting oscillations which resemble the conventional heart sound signals. The existence of Shilnikov type of heteroclinic orbit in the three-dimensional system is proven using the undetermined coefficients method. As a result, Shilnikov criterion guarantees that the three-dimensional system has the horseshoe chaos. The corresponding electronic circuit is designed and implemented, exhibiting experimental chaotic attractors in accord with numerical simulations.


Chaos Bursting oscillations Three-dimensional autonomous chaotic system Electronic implementation Bifurcation Shilnikov criterion 



This work has been partially funded by the European Union under project PHOCUS (EU FET-Open grant: 240763) and by the Research Foundation-Flanders (FWO). This work was supported by the Belgian Science Policy Office under grant “photonics@be”. S.T.K. and P.W. are grateful to the Humbolt Fondation (Germany) for laboratory equipment grant. S.T.K. thanks Professor J.-M. Malasoma (ENTPE, University of Lyon, France) and Professor T. Erneux (ONT, Université Libre de Bruxelles, Belgium) for having kindly provided literature.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Sifeu Takougang Kingni
    • 1
    • 2
  • Lars Keuninckx
    • 1
  • Paul Woafo
    • 2
  • Guy Van der Sande
    • 1
  • Jan Danckaert
    • 1
  1. 1.Applied Physics Research Group (APHY)Vrije Universiteit BrusselBrusselsBelgium
  2. 2.Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of ScienceUniversity of Yaoundé IYaoundéCameroon

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