负参数空间分数阶Chua系统的动力学行为及实验验证  

Dynamics analysis and circuit implementation of fractional-order Chua's system with negative parameters

作　　者：胡串 李志军[1] 陈茜茜[1] 

机构地区：[1]湘潭大学信息工程学院,湘潭411105

出　　处：《物理学报》2017年第23期60-69,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61176032;61471310);湖南省自然科学基金(批准号:2015JJ2142;2015JJ2140)资助的课题~~

摘　　要：Chua系统展现出丰富的动力学行为,易于电路实现,因而成为混沌研究的经典范例.然而,现有针对Chua系统的研究大都局限于系统的正参数空间.基于分数阶的时域求解法,研究了分数阶Chua系统在负参数空间下的动力学行为.采用分数阶稳定性理论分析了系统平衡点的稳定性,用分岔图、最大李雅普诺夫指数研究了系统控制参数和阶次变化时系统的动力学行为.为了实验验证系统的动力学行为,采用运放、电阻、电容等模拟器件实现了负参数空间下的分数阶Chua系统,实验结果与数值仿真结果完全一致.该研究成果对进一步完善Chua系统,推动Chua系统在混沌中的应用具有参考价值.Because of simple schematic structure and complex dynamical behaviors, the Chua＇s system is considered as a paradigm for chaos research. Despite a great many of studies relating to the Chua＇s system, most of them focus on its positive parameter space. This is explained by the fact that the implementation of the Chua＇s circuit with negative parameters needs resistors, inductances and/or capacitors with negative values, and thus leads to physical impossibility. In order to extend the parameter space of the Chua＇s system to its negative side, where all system parameters are negative, an equivalent realization of the Chua＇s circuit is developed with off-the-shelf electronic components by an electronic analogy method. Recently, the research of fractional-order chaotic systems has received considerable interest. However, the theoretical and experimental studies of the fractional-order Chua＇s system with negative parameters are still lacking. In this study, we set up a model of the fractional-order Chua＇s system in negative parameter space. The stability of all equilibrium points is investigated with the fractional-order stability theory. Based on the Grfinwald-Letnikov derivative, the dynamical behaviors dependent on the control parameter and the fractional orders are investigated by standard nonlinear analysis techniques including phase portraits, the largest Lyapunov exponents, and bifurcation diagrams. In order to further verify the dynamic behaviors of the fractional-order Chua＇s system with negative parameters, an experimental implementation of the Chua＇s circuit with negative parameters based on an electronic analogy is performed with off-the-shelf electronic components such as operational amplifiers, resistors and capacitors. The experimental tests are conducted on the resulting circuit. A period-doubling bifurcation route to chaos is successfully observed and some typical phase diagrams are captured by an oscilloscope, which are well consistent with theoretical analyses and numerical simulatio

关 键 词：分数阶 Chua系统 负参数空间 混沌电路 

分 类 号：O415.5[理学—理论物理]