【作者】 王铁邦；

【导师】 陈光旨；

【作者基本信息】 广西大学 ， 理论物理， 2001， 硕士

【摘要】 本文成功地用相互耦合同步法实现了非线性系统中的时空混沌同步、超混沌同步，并探讨了参数不匹配情况下的混沌同步。本文的前两章对混沌理论及控制混沌和混沌同步的发展作了一简要概括，它是我们具体工作（第三章-第五章）的基石。 第三章致力于研究耦合普通微分方程系统的时空混沌同步。我们用相互耦合同步法实现了耦合普通微分方程系统的时空混沌法同步。计算了最大Lyapunov指数谱，讨论并给出了耦合系数与同步时间之间的关系。 第四章侧重于研究超混沌系统的同步。利用相互耦合同步法在超混沌LC振子系统中实现了混沌同步。给出了确定耦合系数的方法，计算了最大Lyapunov指数谱。该方法对参数不匹配具有鲁棒性。 第五章是在第四章的基础上，结合相互耦合同步法和自适应控制同步法实现参数不匹配情况下的混沌系统的精确同步。更多还原

【Abstract】 This paper successfully synchronize spatiotemperal chaos and hyperchaos in nonlinear systems via the mutual coupling method and investigate synchronization in the mismatched parameters circumstance. In the first two chapters, we give a summary of chaos theory and the development of controlling chaos and chaos synchronization, respectively. They are the general bases of our concrete work (chapters to chapter 5).Chapter 3 is devoted to spatiotemperal chaos synchronization in coupled ordinary differential equations (CODE). We realize spatiotemperal chaos in CODE via the mutual coupling method. The largest Lyapunov exponent spectra are calculated. And the connection between the coupling parameter and the synchronization time is discussed and given.Chapter 4 emphasizes on synchronizing hyperchaos. The hyperchaotic synchronization is achieved in LC oscillator via the mutual coupling method. The method to confirm coupling coefficient is given, the largest Lyapunov exponent spectra are calculated, and the connection between the coupling parameter and the synchronization time is discussed and given. This method is robust to the mismatched parameters.In chapter 5, we combine the mutual coupling method and adaptive method to realize complete synchronization in the mismatched parameter circumstance on the base of chapter 4.更多还原