中文摘要：

为了产生复杂的混沌吸引子,构造了一个新的三维二次自治混沌系统.该系统含有三个参数,每一个方程含有一个非线性乘积项.利用理论推导、数值仿真、Lyapunov指数谱和分岔图对系统的基本动力学特性进行了分析.结果表明,该系统具有五个平衡点,因而与Lorenz,Rosslor,Chen、Lu等混沌系统是非拓扑等价的;当其参数满足一定条件时,系统是混沌的.与Lorenz等混沌系统相比,该系统具有更大的正Lyapunov指数,能够产生复杂的混沌吸引子和一些有趣的动力学行为.最后,设计了实现该系统的混沌电路,电路实验结果与动力学特性分析、数值仿真完全相符,从而验证了系统的混沌行为.

英文摘要：

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.