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.