Constructing Chaotic Systems with Conditional Symmetry

Chunbiao Li
Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China
Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China

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

Hongyan Xing
Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China
Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received: 29 July 2016 / Accepted: 27 September 2016 / Published online: 6 October 2016

ABSTRACT

Asymmetric dynamical systems sometimes admit a symmetric pair of coexisting attractors for reasons that are not readily apparent. This phenomenon is called conditional symmetry and deserves further explanation and exploration. In this paper, a general method for constructing such systems is proposed in which the asymmetric system restores its original equation when some of the variables are subjected to a symmetric coordinate transformation combined with a special offset boosting. Two regimes of this conditional symmetry are illustrated in chaotic flows where a symmetric pair of attractors resides in asymmetric basins of attraction.