Dissipative chaos, Shilnikov chaos and bursting oscillations in a three-dimensional autonomous system: theory and electronic implementation |
| |
Authors: | Sifeu Takougang Kingni Lars Keuninckx Paul Woafo Guy Van der Sande Jan Danckaert |
| |
Affiliation: | 1. Applied Physics Research Group (APHY), Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium 2. Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of Science, University of Yaoundé I, Po. Box 812, Yaoundé, Cameroon
|
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|