中国物理B ›› 2008, Vol. 17 ›› Issue (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

何大韧1, 屈世显2, 卢永智2, 张林2   

  1. (1)College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China; (2)Institute of Theoretical & Computational Physics, School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
  • 收稿日期:2008-03-18 修回日期:2008-03-26 出版日期:2008-12-20 发布日期:2008-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10275053).

Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap

Qu Shi-Xian (屈世显)a,  Lu Yong-Zhi(卢永智)b, Zhang Lin (张林)b, He Da-Ren (何大韧)b   

  1. a Institute of Theoretical & Computational Physics, School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China; b College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China
  • Received:2008-03-18 Revised:2008-03-26 Online:2008-12-20 Published:2008-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10275053).

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摘要： 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.

关键词: coexistence of attractors, piecewise linear map, mapping hole, discontinuous bifurcation

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.

Key words: coexistence of attractors, piecewise linear map, mapping hole, discontinuous bifurcation

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.45.Gg (Control of chaos, applications of chaos)