Oscillatory Dynamics in Complex Recurrent Neural Networks

Spontaneous oscillations measured by local field potentials (LFPs), electroencephalograms and magnetoencephalograms exhibit a variety of oscillations spanning the frequency band of 1–100[Formula: see text]Hz in animals and humans. Both instantaneous power and phase of these ongoing oscillations have commonly been observed to correlate with pre-stimulus processing in animals and humans. However, despite numerous attempts it is not fully clear whether the same mechanisms can give rise to a range of oscillations as observed in vivo during resting-state spontaneous oscillatory activity of the brain. In this paper, we show how oscillatory activity can arise out of general recurrent on-center off-surround neural network. This work shows that (a) a complex-valued input to a class of biologically inspired recurrent neural networks can be shown to be mathematically equivalent to a combination of real-valued recurrent networks with real-valued feed-forward network, and (b) such a network can give rise to oscillatory signatures. We also validate the conjecture with results of simulation of complex-valued additive recurrent neural network.