  An open problem in neuroscience is to explain the functional role of
oscillations in neural networks, contributing, for example, to perception,
attention, and memory. Cross-frequency coupling (CFC) is associated with
information integration across populations of neurons. Impaired CFC is linked
to neurological disease. It is unclear what role CFC has in information
processing and brain functional connectivity. We construct a model of CFC which
predicts a computational role for observed $\theta - \gamma$ oscillatory
circuits in the hippocampus and cortex. Our model predicts that the complex
dynamics in recurrent and feedforward networks of coupled oscillators performs
robust information storage and pattern retrieval. Based on phasor associative
memories (PAM), we present a novel oscillator neural network (ONN) model that
includes subharmonic injection locking (SHIL) and which reproduces experimental
observations of CFC. We show that the presence of CFC increases the memory
capacity of a population of neurons connected by plastic synapses. CFC enables
error-free pattern retrieval whereas pattern retrieval fails without CFC. In
addition, the trade-offs between sparse connectivity, capacity, and information
per connection are identified. The associative memory is based on a
complex-valued neural network, or phasor neural network (PNN). We show that for
values of $Q$ which are the same as the ratio of $\gamma$ to $\theta$
oscillations observed in the hippocampus and the cortex, the associative memory
achieves greater capacity and information storage than previous models. The
novel contributions of this work are providing a computational framework based
on oscillator dynamics which predicts the functional role of neural
oscillations and connecting concepts in neural network theory and dynamical
system theory.
