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

Julien Clinton Sprott
Department of Physics, University of Wisconsin–Madison,
Madison, WI 53706, USA

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

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.

Ref: C. Li, J. C. Sprott, and Y. Liu, International Journal of Bifurcation and Chaos 30, 2050067-1-12 (2020)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.