Time-Reversible Chaotic System
with 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
Received March 7, 2019; Revised September 14, 2019
When the polarity reversal induced by offset
boosting is considered, a new regime of a timereversible chaotic
system with conditional symmetry is found, and some new
time-reversible systems are revealed based on multiple
dimensional offset boosting. Numerical analysis shows that the
system attractor and repellor have their own dynamics in
respective time domains which constitutes the fundamental
property in a time-reversible system. More remarkably, when the
conditional symmetry is destroyed by a slightly mismatched
offset controller, the system undergoes different bifurcations
to chaos, and the corresponding coexisting attractors and
repellors
shape their own phase trajectories.