Chaotic flows with a single nonquadratic term

Chunbiao Li^a,^b,c,∗, J.C.Sprott^b

^aEngineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 210007, China
^bDepartment of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
^cSchool of Information Science and Engineering, Southeast University, Nanjing 210096, China

Received 16 August 2013
Received in revised form 4 November 2013
Accepted 7 November 2013
Available online 15 November 2013
Communicated by C.R. Doering

This paper addresses a previously unexplored regime of three-dimensional dissipative chaotic flows in which all but one of the nonlinearities are quadratic. The simplest such systems are determined, and their equilibria and stability are described. These systems often have one or more infinite lines of equilibrium points and sometimes haves stable equilibria that coexist with the strange attractors, which are sometimes hidden. Furthermore, the coefficient of the single nonquadratic term provides a simple means for scaling the amplitude and frequency of the system.