Populations of heterogeneous phase oscillators with frustrated random interactions exhibit a
quasiglassy state in which the distribution of local fields is volcanoshaped. In a recent work …

We consider a next generation neural field model which describes the dynamics of a
network of theta neurons on a ring. For some parameters the network supports stable time …

We develop a circular cumulant representation for the recurrent network of quadratic
integrate-and-fire neurons subject to noise. The synaptic coupling is global or …

Large collections of coupled, heterogeneous agents can manifest complex dynamical
behavior presenting difficulties for simulation and analysis. However, if the collective …

We consider directed networks of Winfree oscillators with power law distributed in-and out-
degree distributions. Gaussian and power law distributed intrinsic frequencies are …

We consider large networks of theta neurons and use the Ott-Antonsen ansatz to derive
degree-based mean-field equations governing the expected dynamics of the networks …

In this dissertation we develop a suite of data-driven modeling techniques for dynamical
systems by leveraging manifold learning, dimensionality reduction, and deep learning …