Emergence dynamics under unequal coupling and asymmetric noise

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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.