A fully qualified four-wing four-dimensional autonomous chaotic system and its synchronization

In order to generate a real four-wing chaotic attractor, a new four-dimensional (4D) smooth quadratic autonomous system which is constructed by a linear controller to a three-dimensional (3D) pseudo four-wing system is proposed in this paper. Some complex dynamical behaviors such as equilibrium points and chaos are investigated and analyzed. The corresponding four-wing chaotic attractor is first numerically verified through investigating phase trajectories, Lyapunove exponents, bifurcation diagram, analysis of power spectrum and Poincaré maps. Furthermore, an oscillator circuit is designed for implementation, with Multisim observations for verification and demonstration. Finally, an extended synchronization approach is proposed for synchronizing the four-wing chaotic system. On the basis of Jacobin matrix method, it is not necessary to construct the Lyapunov functions, which makes this scheme simpler. Theoretical analysis and numerical simulations demonstrate the validity and feasibility of the proposed control method.