Offset Boosting for Breeding Conditional Symmetry
Chunbiao Li∗
Jiangsu Collaborative Innovation Center of Atmospheric
Environment and
Equipment Technology (CICAEET), Nanjing University of
Information
Science and Technology, Nanjing 210044, P. R. China
Jiangsu Key Laboratory of Meteorological Observation
and Information Processing, Nanjing University
of Information Science and Technology,
Nanjing 210044, P. R. China
goontry@126.com
chunbiaolee@nuist.edu.cn
Julien Clinton Sprott
Department of Physics, University of Wisconsin–Madison,
Madison, WI 53706, USA
sprott@physics.wisc.edu
Yongjian Liu
Guangxi Colleges and Universities Key Laboratory
of Complex System Optimization and Big Data Processing,
Yulin Normal University, Yulin, Guangxi 537000, P. R. China
liuyongjianmaths@126.com
Zhenyu Gu† and Jingwei Zhang‡
Jiangsu Key Laboratory of Meteorological Observation
and Information Processing, Nanjing University
of Information Science and Technology,
Nanjing 210044, P. R. China
School of Electronic and Information Engineering,
Nanjing University of Information Science and Technology,
Nanjing 210044, P. R. China
†gzy1210440@163.com
‡20151305061@nuist.edu.cn
Received April 27, 2018; Revised July 5, 2018
Symmetry is usually prevented by the broken
balance in polarity. If the offset boosting returns the balance
of polarity when some of the variables have their polarity
reversed, the corresponding system becomes conditionally
symmetric and in turn produces coexisting attractors with that
type of symmetry. In this paper, offset boosting in one
dimension or in two dimensions in a
3D system is made for producing conditional symmetry, where the
symmetric pair of coexisting attractors exist from
one-dimensional or two-dimensional offset boosting, which is
identified by the basin of attraction. The polarity revision
from offset boosting provides a general method for constructing
chaotic systems with conditional symmetry. Circuit
implementation based on FPGA verifies the coexisting attractors
with conditional symmetry.
Ref: C. Li, J. C. Sprott, Y. Liu, Z.
Gu, and J. Zhang, International Journal of Bifurcation and Chaos 28, 185013-1-13 (2018)
The complete paper is available in
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