Emergence dynamics under unequal coupling and asymmetric noise

物理学、化学和生物学中的许多复杂系统都可以看作是相互作用的振荡器网络。更重要的是，这些网络如何执行其功能取决于耦合振荡器的集体动力学。同步性和连贯性是这种集体行为的两个最突出的例子。两个普遍存在的成分，耦合和噪声，可以驱动复杂网络表现出新的和意想不到的集体活动（即涌现动力学）。因此，我的研究计划的长期目标是研究耦合，噪声和单个振荡器的内在特性的相互作用如何塑造复杂系统的涌现动力学。等耦合（即均匀耦合）和对称噪声（即等噪声强度）的作用已经得到了很好的研究。但不均匀耦合和非对称噪声的一般机制尚不清楚。此外，许多神经系统的实验研究表明，复杂网络包含一些显著重复的模体，这些模体被认为是这些网络的基本构建块。包含两个或三个神经元的网络模体明显多于其他多神经元模体。这样的网络拓扑结构也在其他领域中发现，例如电气工程。因此，未来五年的短期目标是研究不相等的耦合强度和不对称噪声的同时相互作用如何塑造（1）2-振荡器基序，（2）3-振荡器基序和（3）具有高度聚集的2-和3-振荡器模块的网络的出现动力学。该研究的成功完成将促进动力系统理论的基础知识。理解驱动涌现动力学形成的机制是发现复杂网络功能并进一步开发控制它们的潜在方法的关键。该研究计划将培养HQP与可转移的数学和计算技能，为未来在学术界或工业界的成功。

Many complex systems in physics, chemistry and biology can be seen as networks of interacting oscillators. More importantly, how these networks perform their functions depends on the collective dynamics of the coupled oscillators. Synchrony and coherence are two of the most prominent examples of such collective behavior. Two ubiquitous components, the coupling and noise, may drive the complex networks to exhibit new and unexpected collective activities (i.e. emergence dynamics). Hence, the long-term objective of my research program is to investigate how the interplay of coupling, noise and intrinsic characteristics of individual oscillators shape the emergence dynamics of complex systems. The roles of equal coupling (i.e. uniform coupling) and symmetric noise (i.e. equal noise intensity) have been well studied. But the general mechanisms of unequal coupling and asymmetric noise are not clear yet. Furthermore, many experimental studies in nervous systems have reported that complex networks contain some significantly recurring motifs which are believed to be basic building blocks of these networks. The network motifs containing two or three neurons are significantly more than other multi-neuron motifs. Such network topology has also be found in other fields, such as electrical engineering. Therefore, the short-term objectives in the next five year are to study how the simultaneous interplay of unequal coupling strength and asymmetric noise shape the emergence dynamics of (1) 2-oscillator motifs, (2) 3-oscillator motifs, and (3) the networks with highly clustered 2- and 3-oscillator modules. The successful completion of the proposed research will advance the fundamental knowledge in dynamical systems theory. Understanding the mechanisms driving the formation of emergent dynamics is the key to discover the functions of complex networks and further develop potential ways of controlling them. This research program will train HQP with transferable mathematical and computational skills for future success in academia or industry.