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Chin. Phys. B, 2008, Vol. 17(12): 4418-4423    DOI: 10.1088/1674-1056/17/12/014
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Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap

He Da-Rena, Qu Shi-Xianb, Lu Yong-Zhib, Zhang Linb
a College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China; b Institute of Theoretical & Computational Physics, School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
Abstract  Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-11, period-6, chaotic band-12 and band-6 attractors. They are induced by different mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.
Keywords:  discontinuous bifurcation      coexistence of attractors      piecewise linear map      mapping hole     
Received:  18 March 2008      Published:  20 December 2008
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10275053).

Cite this article: 

He Da-Ren, Qu Shi-Xian, Lu Yong-Zhi, Zhang Lin Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap 2008 Chin. Phys. B 17 4418

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