不确定分数阶Colpitts系统的混沌同步研究

摘要

分数阶混沌系统在信息加密等领域具有广泛的研究价值.通过理论推导和数值仿真两方面的研究,采用分数阶系统的稳定性定理,对选取的分数阶多涡卷混沌Colpitts振荡电路系统的动力学特性进行了详细的分析,并计算出了该系统处于混沌态时的阶数范围.研究结果证明,当系统作混沌运动时,其混沌吸引子的形态存在特殊的演变过程,逐渐从单涡卷混沌吸引子演变为多涡卷混沌吸引子.将自适应技术和参数辨识技术应用到混沌系统的同步控制中,在参数不确定的情况下,基于Lyapunov函数稳定性理论,设计了合理的控制器和估计参数自适应律.利用不确定参数的自适应同步法,分别实现了系统在阶数相同和阶数不同两种情况下的完全同步以及对未知参数的辨识.该结果对于参数未知混沌系统的同步研究具有重要意义.%In information encryption field,the fractional-order chaotic systems have extensive research value.Through the research on theoretical derivation and numerical simulation,by adopting the stability theorem of fractional-order system,the dynamics characteristics of the selected fractional-order multi-scroll chaotic Colpittsoscillation circuit system are analyzed in detail,and the range of the orders in which the systemis in a chaotic state is calculated.The results of research show that when the system is in chaotic motion,the form of the chaotic attractor has a specific transformation process;the single-scroll chaotic attractor gradually turns into multi-scroll chaotic attractor.Adaptive control technology and parameter identification technology are used in the synchronous control of chaotic systems,in the case of uncertain parameters,and based on the Lyapunov stability theory;a reasonable controller is designed,and the parameter adaptive laws are estimated.By using the adaptive synchronization under uncertain parameters,the full synchronization of the fractional-order chaotic systems with the same order and a different order and the identification of the unknown parameter are realized respectively.The results are more useful for researching the synchronization of chaotic systems with unknown parameters.