没有线性项的混沌系统分析与电路设计  

Analysis and Circuit Design of a Chaotic System with No Linear Term

作　　者：徐启程[1] 孙常春[1] 何凯[2] XU Qi-cheng;SUN Chang-chun;HE Kai(School of Science,Shenyang Jianzhu University,Shenyang 110168,China;School of Information and Control Engineering,Shenyang Jianzhu University,Shenyang 110168,China)

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]沈阳建筑大学信息与控制工程学院,辽宁沈阳110168

出　　处：《控制工程》2022年第7期1227-1231,共5页Control Engineering of China

基　　金：辽宁省教育厅自然科学基金资助项目(lnqn201919)。

摘　　要：构造了一个没有线性项的新三维连续自治混沌系统,该系统仅由非线性项和常数项构成,一个非线性项是指数小于1的复合幂函数,通过调节参数,系统能生成两种不同类型的吸引子,即隐藏吸引子和自激吸引子。同时,对系统的复杂动力学行为进行了详细分析,包括平衡点的类型、Lyapunov指数谱、分岔图和庞加莱映射等,结果表明此系统具有混沌特性。最后,针对此混沌系统,进行了相应的电路设计,仿真结果验证了理论分析的正确性。A new three-dimensional continuous autonomous chaotic system with no linear term is constructed in this paper.The system consists only of nonlinear terms and constant terms.A nonlinear term is a compound power function with an exponent less than 1.By modulating the parameters,the system can generate two different types of attractors including hidden attractors and self-excited attractors.Simultaneously,complex dynamical behaviors including the type of each equilibrium point,Lyapunov exponential spectrum,bifurcation diagram and Poincaré map of the system are analyzed in detail.The results show that the system has chaotic characteristics.Finally,corresponding circuit design of the chaotic system is carried out.The simulation results verify the validity of the theoretical analysis.

关 键 词：混沌系统 复合幂函数 隐藏吸引子 电路设计 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]