Despite the common belief that individual differences are detrimental to uniform group dynamics, the opposite can be true and, in fact, quite common. One major theme of my research is to understand when and why uniformity can grow out of diversity in coupled systems.
Complex networks often support complex synchronization patterns. Understanding such patterns will enable us to manipulate the behavior of numerous biological, social, and technological systems. I work on general theories and efficient algorithms to identify, characterize, and control synchronization patterns in both traditional and generalized networks.
One particularly interesting type of synchronization patterns is chimera states, where a network of identically coupled identical oscillators spontaneously splits into coherent and incoherent clusters. It represents symmetry breaking phenomena in networks. I contribute to the understanding of chimera states by characterizing new chimeras and proposing general mechanisms giving rise to such states.
How do basins look like in high-dimensional dynamical systems? A deeper understanding of this question can lead to new insights on systems such as power grids and neural networks. We explore basin geometries in high-dimensional systems and their implications.
Networks offer a versatile description of interconnected complex systems. However, the original formulation of a static network representing a single type of pairwise interaction has its limitations. I explore collective dynamics on various models that go beyond standard networks (e.g., hypergraphs) and characterize the effects of higher-order structures such as nonpairwise interactions and temporal interactions.