Elementary quadratic chaotic flows with a single non-hyperbolic equilibrium

• A kind of jerk equations are proposed.
• Chaos can occur with all types of a non-hyperbolic equilibrium.
• The mechanism of generating chaos is discussed.
• Feigenbaum's constant explains the identified chaotic flows.

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.