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.
Received: 18 March 2008
Published: 20 December 2008
(Numerical simulations of chaotic systems)
(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