【作者】 钱郁；

【导师】 陈光旨；

【作者基本信息】 广西大学 ， 理论物理， 2007， 硕士

【摘要】 斑图是在空间或时间上具有某种规律性的非均匀宏观结构，普遍存在于自然界中。螺旋波是非平衡斑图中最常见的一种，在自然界中广泛存在，可以在振荡系统、激发系统和双稳系统中观察到，包括许多物理、生物、化学等系统。由于在很多实际系统中螺旋波及其破碎是有害的，例如，在心肌中，螺旋波是导致心动过速的主要原因；螺旋波的自发破碎会导致心室失颤。因此，开展对螺旋波的失稳机制以及螺旋波和时空混沌的控制研究具有十分重要的意义。本文重点研究了螺旋波和时空混沌的控制，特别是通过互耦合及驱动耦合的方法来研究其对螺旋波和时空混沌的控制效果。论文的第一章重点介绍了什么是可激发系统、一些可激发系统模型以及目前成熟的关于螺旋波动力学行为和螺旋波破碎的理论。第二章重点讨论了螺旋波和时空混沌的控制和同步。我们从引入反馈控制法、外力控制法和调整参数控制法对可激发系统中的螺旋波和时空混沌控制进行归类。对于时空斑图的同步讨论，主要集中在双层耦合可激发模型。第三章主要研究了两个相互耦合的可激发系统时空混沌的同步行为。我们通过相互耦合的方法实现了两个可激发系统时空混沌的完全同步。给出了确定耦合系数的方法，得出了能使两个可激发系统时空混沌同步所需要的耦合系数的阈值。基于相互耦合法，将时空混沌态系统与静息态系统进行相互耦合，实现了将时空混沌控制成静息态；将时空混沌态系统与外周期力控制系统进行相互耦合，在一定的参数区域内（0.065≤ε≤0.090），实现了只需微调已知外周期力参数w，便可将该参数区域内时空混沌控制成靶波态。第四章主要研究了驱动耦合控制法对可激发介质中螺旋波的控制效果。研究结果显示，这种控制方法具有教高的控制效率及鲁棒性，即既能控制CO在铂（Pt110）表面氧化反应中的螺旋波，又能控制FHN模型中的螺旋波。对于不同的模型，我们发现最小控制时步n与耦合系数c之间存在形如n～c^-k的幂指数关系。更多还原

【Abstract】 Pattern is a kind of inhomogeneous, spatiotemporal macro-structure with some laws, to exist in a large number of systems in nature. Spiral wave is a kind of nonequilibrium pattern, which can be found in excitable media, oscillatory media, and bistable（more precisely double metastable） media, including a lot of physical, biological and chemical systems. In some cases spiral waves and spatiotemporal chaos are undesirable because of their harmfulness. Such as the spiral waves in cardiac muscle can be a cause of tachycardia. Repetitious breakup of spiral waves can lead to spatiotemporal chaos, which is believed as a mechanism of ventricular fibrillation （VF）. Therefore, effective control methods are needed to control spiral waves and spatiotemporal chaos. In this master thesis, we focus on the study of spiral waves and spatiotemporal chaos control in excitable media by using mutual coupling method and unidirectional coupling method.The first chapter mainly reviews the excitable systems, some models and the recent development about the dynamics and the breakup of spiral waves.The second chapter discusses the control and synchronization of spiral waves and spatiotemporal chaos. Three control methods have been mentioned, such as feedback control method, outside force control method and parameter adjustment control method. The synchronization of spatiotemporal pattern also has been discussed especially focused in two layer coupled excitable model.The third chapter gives a systematic research of the effects of the mutual coupling method on the spatiotemporal chaos synchronization behavior. Complete synchronization can be achieved by using this method. The method to calculate the coupling coefficient is given and the suitable coupling coefficient which complete synchronization can be achieved has been attained. Spatiotemporal chaos is suppressed in two ways by coupling with two systems in different states.The effects of unidirectional coupling method to suppress spiral waves in excitable media are studied in the forth chapter. It is found that this control method has high control efficiency and robust. It adapts to control spiral waves for catalytic CO oxidation on platinum as well as for the FHN model. And the power law n～c^-k of control time steps n versus the coupling strength c for different model has been obtained.更多还原