期刊
NONLINEAR DYNAMICS
卷 73, 期 1-2, 页码 1111-1123出版社
SPRINGER
DOI: 10.1007/s11071-013-0856-1
关键词
Chaos; Bursting oscillations; Three-dimensional autonomous chaotic system; Electronic implementation; Bifurcation; Shilnikov criterion
资金
- European Union under project PHOCUS (EU FET) [240763]
- Research Foundation-Flanders (FWO)
- Belgian Science Policy Office
- Humbolt Fondation (Germany)
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.
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