对动力学系统同步现象与斑图现象的研究很早就成为物理学研究的重要课题。人们对于非线性动力学系统中混沌现象的研究贯穿了二十世纪的后半叶，它至今仍是物理学及交叉科学研究的活跃领域之一。1990年Pecora与Carroll在《物理评论快报》发表了两耦合混沌振子的混沌同步概念之后，对混沌同步的研究热潮蓬勃展开。随着对自然的认识逐渐加深，研究从线性到非线性、从少自由度到多自由度一步步发展，充满了复杂性。而网络的方法，正是人们获得的研究复杂性的新的科学方法。人们运用非线性动力学去透视，去探讨网络的动力学性质。对于物理学家而言，研究复杂网络的目标之一是理解网络拓扑结构对物理过程的影响，网络的同步正是在网络的拓扑性质和网络的功能之间搭起了一座桥梁。本文通过对于耦合非线性时空网络的同步现象与斑图现象的研究来理解网络中的合作行为。第一章简单回顾了非线性科学中混沌系统与时空网络这两大类发展的历史与现状，对混沌系统以完全同步、相同步为代表的混沌同步现象的产生和性质加以描述，并着重介绍了在网络尤其是群结构的时空网络中的同步这一领域已有的工作。在第二章中我们详细的介绍了群结构时空网络中的同步现象。运用线性稳定性分析和极限的方法，我们得到了时空网络中群同步的本征值关系、拓扑条件以及 比值条件。给出了判断时空网络中是否能够发生群同步的方法，并且完全从理论上证明了这一方法，在具体的一般的网络中证明了这种方法。在群结构的时空网络中，我们发现了小集团(bloc)结构的重要性，通过它们，我们可以决定如何在各个群之间加入连接才能达到群同步以及达到群同步的最好的连接方式；通过观察其中的最大的小集团(bloc)，我们可以判断群同步发生的临界耦合强度。进一步，研究时空网络的动力学情况，我们得到 相空间，整个时空网络存在五个状态：完全不同步状态(US)，群同步状态(GrS) ，群内同步状态(IS)，完全同步状态(CS)和过渡状态。当把两个群构成的网络扩展到多个群，扩展到整个二维时空，我们可以看到不同的斑图转换，得到网络从完全不同步到完全同步的多种路径。第三章研究了二维耦合混沌系统出现的条纹状斑图行为，发现斑图的出现非常依赖于系统的扩散系数等参数匹配和系统的初始状态。我们运用线性稳定性分析方法，完全理论上给出了斑图的出现条件及出现形式，并取得了实验上的验证。第四章我们研究了噪声驱动可激发系统的相干共振和相锁频现象。揭示了可激发系统中的相干共振和相同步。通过研究噪声对可激发振子的作用，我们揭示了内在本征频率和噪声导致的相锁频之间的重要关系。我们提出的这个动力学机制是普遍的，给出了不稳定模的存在。最后，我们对全文进行总结。

The studies of synchronization phenomena and pattern phenomena have been subjects of great interest since the earlier days of physics. The studies of chaotic phenomena in nonlinear dynamical systems were through the second half of the 20th century, which is still one of active fields in physics and related interdisciplinary fields. Since in 1990 Pecora and Carroll published Synchronization in chaotic systems in Physics Review Letter, chaos synchronization has become a significant topic. There is more and more complexity when people try to recognize the nature. The method of network is just the way for people to study the complexity of the world. People use nonlinear dynamics to discuss the dynamics of networks. For physicists, it is one of the aims to understand how the topology impacts the physical process on networks. Synchronization on networks is just a bridge between the topology and the function on networks. In this paper, we study synchronization phenomena and pattern phenomena on coupled nonlinear networks to understand the cooperative behaviors on networks.In Chapter I, we briefly review the history and current progresses on studies of chaotic system and spatial-temporal networks. Different types of chaos synchronization including complete synchronization, partial synchronization are discussed. And some works about synchronization on networks are retrospected and discussed.In Chapter II, the idea of group synchronization(GrS) are introduced and described. Using linear stability analysis and asymptotic method, we obtain theoretically the criterions for GrS and verify them for more general networks. In particular, note that for a group-structure network, the key characters are the number and the size of open-blocs and close-blocs and the relation between the intragroup coupling and the intergroup connection r. Our results concern how the network synchronization ability depends on these characters. We find that different topologies of intergroup couplings may lead to different synchronization ability. We find the optimal way to get group synchronization. The analytical treatment reveal the transitions of synchronous regimes. We get the " ¡ r phase diagram space. The phase diagram space is divided into five regimes: the unsynchronized state (US), the state of synchronization between groups (GrS), the state of synchronization inside the individual group (IS), the state of complete synchronization (CS) and the transition state. When we expand the network with two groups structure to spatial-temporal networks, we can find transitions between different patterns.In Chapter III, we study the stripe patterns in coupled chaotic systems and find the emergence of patterns greatly depends on the initial states and the matching of diffusive parameters. Furthermore, we get the condition of the form of the stripe patterns by using stability analysis, which is in accordance with the numerical experiments.In Chapter IV, we study the coherent resonance and phase locking in noise-driven excitable systems. By considering the FitzHugh-Nagumo neuron model, we discuss the relation between the intrinsic natural frequency and noise-induced ¯rings. The mechanism we proposed in this paper is generic, given that an unstable mode exists and can be excited by external drivings. Moreover, the mechanism and results we proposed here can be expected to be well extended to studies in neurophysiology and other related topics.A summary is given at the end of the dissertation.