Analysis and Control of a Three-Dimensional Quadratic Polynomial System with No Equilibrium Point and No Linear Term

A three-dimensional quadratic polynomial system with no equilibrium point and no linear term is derived in this paper. A new chaotic attractor can be generated from the system. Moreover, the existence of chaos is verified by calculating three Lyapunov exponents. Dynamical behaviors of the system are analyzed in detail. The system does not have any equilibrium point. The attractor generated from the system belongs to one of hidden attractors. Bifurcation diagrams of states are depicted respectively with the variation of two parameters. A problem on control of the polynomial system is investigated by employing constant control and state feedback. Another polynomial system with double symmetrical parameters is reported further.