Elementary Quadratic Chaotic Flows with a Single Non-hyperbolic Equilibrium

Zhouchao Wei
School of Mathematics and Physics, China University of Geosciences, Wuhan, 530074, PR China
College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, PR China
Mathematical Institute, University of Oxford, Oxford, UK

J. C. Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706, USA

Huai Chen
Faculty of Earth Sciences, China University of Geosciences, Wuhan, 530074, PR China

Received 17 February 2015
Received in revised form 26 April 2015
Accepted 16 June 2015
Available online 22 June 2015
Communicated by A. P. Fordy

This paper describes a class of third-order explicit autonomous differential equations, called jerk equations, with quadratic nonlinearities that can generate a catalog of nine elementary dissipative chaotic flows with the unusual feature of having a single non-hyperbolic equilibrium. They represent an interesting sub-class of dynamical systems that can exhibit many major features of regular and chaotic motion. The proposed systems are investigated through numerical simulations and theoretical analysis. For these jerk dynamical systems, a certain amount of nonlinearity is sufficient to produce chaos through a sequence of period-doubling bifurcations.

Ref: Z. Wei, J. C. Sprott, and H. Chen, Phys. Lett. A 379, 2184-2187 (2015)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.