Journal
NONLINEAR DYNAMICS
Volume 83, Issue 1-2, Pages 623-630Publisher
SPRINGER
DOI: 10.1007/s11071-015-2352-2
Keywords
Chaos; Poincare map; Topological horseshoe; Topological entropy; Chaotic circuit
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Funding
- Natural Science Foundation of China [61203138, 61374169]
- Development of Science and Technology Foundation of the Higher Education Institutions of Tianjin [20120829]
- Science and Technology Talent and Technology Innovation Foundation of Tianjin, China [20130830]
- Second Level Candidates of 131 Innovative Talents Training Project of Tianjin, China [20130115]
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For a three-dimensional autonomous four-wing chaotic attractor, this paper rigorously verifies its chaotic properties by using topological horseshoe theory and numerical calculations. Firstly, an appropriate Poincar, section of the chaotic attractor is selected by numerical analysis. Accordingly, a certain first return Poincar, map is defined in the Poincar, section. Thereafter, by utilizing numerical calculations and topological horseshoe theory, a one-dimensional tensile topological horseshoe in the Poincar, section is discovered, which revealed that the four-wing attractor has a positive topological entropy, and verifies the existence of chaos in this four-wing attractor. Finally, by using a FPGA chip, the four-wing chaotic attractor was physically implemented, which is more suitable for engineering applications.
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