A new three-dimensional quadratic chaotic system and its circuitry implementation
一个新的三维二次混沌系统及其电路实现

In order to generate complex chaotic attractors, we construct a new three-dimensional quadratic autonomous chaotic system, in which each equation contains a single quadratic cross-product term and a system parameter. Basic dynamic properties of the new system are investigated via theoretical analysis and numerical simulation using the Lyapunov exponent spectrum and bifurcation diagram. Our results show that this system has five equilibria, therefore is not topologically equivalent to the Lorenz, Roesslor or the Chen and Lti systems, and the new system is chaotic when its parameters satisfy certain conditions. Compared with the systems mentioned above, the proposed system has larger positive Lyapunov exponent, displays a complex attractor and some other interesting properties. An electronic circuit was designed to realize the new chaotic system. Experimental chaotic behaviors of the system were found to be identical to the dynamic properties predicted by theoretical analysis and numerical simulations.