Analysis of Gradient Frequency Neural Networks

Stability analysis of supercritical Hopf oscillator (Frontiers 2015 paper)

To model nonlinear transformation of acoustic signals into neural patterns in the auditory system, we use a canonical model for gradient frequency neural networks (GrFNNs), a mathematical model that captures essential properties shared by such networks, regardless of their scale and biophysical mechanisms. Although it is a simple model, its behavior is complex and difficult to analyze because it consists of multiple components with distinct dynamics (e.g., autonomous dynamics, external driving, coupling interaction, plasticity). Our approach is to analyze individual network components separately and attempt to understand the overall dynamics of the model by combining component dynamics. We developed GrFNN Toolbox for simulating and analyzing gradient frequency neural networks. A MATLAB version of the toolbox is available on GitHub [link].

Kim, J. C., & Large, E. W. (book in preparation). Signal processing, plasticity and pattern formation in networks of neural oscillators.

Kim, J. C., & Large, E. W. (2019). Mode locking in periodically forced gradient frequency neural networks. Physical Review E, 99(2), 022421. [pdf]

Kim, J. C., & Large, E. W. (2015). Signal processing in periodically forced gradient frequency neural networks. Frontiers in Computational Neuroscience, 9:152. [link]