How does a pattern of connectivity lead to the emergence of spatiotemoral dynamics in a network? This question becomes quite hard to answer when we consider nonlinear interactions in the system. Further, this problem is even more complicated when we consider time delays in the coupling, which is present in many natural systems. To address this open problem, my research considers operator-based descriptions of finite networks of coupled oscillators, which offers a direct connection between the network adjacency matrix and time delays with the emergent dynamics in the system. This approach has many direct applications to study artificial and biological neural networks, where new analytical approaches are now available.
Main results:
Unified geometric perspective on synchronization phenomena
R. C. Budzinski*, T. T. Nguyen* et al., Chaos (Fast Track) 32 (3), 031104, 2022. (link)
Analytical approach for networks with heterogeneous time delays
R. C. Budzinski*, T. T. Nguyen*, G. Benigno* et al., Physical Review Research 5 (1), 013159, 2023. (link)
Theory of transient chimeras in finite networks
R. C. Budzinski et al., arXiv:2311.01382. (link)