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Abstract
We investigate a discrete-time network model composed of excitatory and inhibitory neurons and dynamic synapses with the aim at revealing dynamical properties behind oscillatory phenomena possibly related to brain functions. We use a stochastic neural network model to derive the corresponding macroscopic mean field dynamics, and subsequently analyze the dynamical properties of the network. In addition to slow and fast oscillations arising from excitatory and inhibitory networks, respectively, we show that the interaction between these two networks generates phase-amplitude cross-frequency coupling (CFC), in which multiple different frequency components coexist and the amplitude of the fast oscillation is modulated by the phase of the slow oscillation. Furthermore, we clarify the detailed properties of the oscillatory phenomena by applying the bifurcation analysis to the mean field model, and accordingly show that the intermittent and the continuous CFCs can be characterized by an aperiodic orbit on a closed curve and one on a torus, respectively. These two CFC modes switch depending on the coupling strength from the excitatory to inhibitory networks, via the saddle-node cycle bifurcation of a one-dimensional torus in map (MT1SNC), and may be associated with the function of multi-item representation. We believe that the present model might have potential for studying possible functional roles of phase-amplitude CFC in the cerebral cortex.
Highlights
Neurons in the brain, process information through diverse neural dynamics emergent from interactions among neurons via synapses
How neural networks formed by the interactions can generate functional dynamics, such as oscillatory or synchronized activity and cross-frequency coupling (CFC), largely remains to be explored
The bifurcation analysis focuses on two types of dynamic synapses, namely short-term depression and facilitation synapses, where τRξ has been fixed at 70 and τFξ ranges between 1 and 140 for the sake of simplicity
Summary
Process information through diverse neural dynamics emergent from interactions among neurons via synapses. How neural networks formed by the interactions can generate functional dynamics, such as oscillatory or synchronized activity and cross-frequency coupling (CFC), largely remains to be explored. The recorded neural activity represents various types of oscillatory waveforms and can be categorized according to the frequency, whose bands, for example, theta and gamma bands, can temporally coexist in the same or different brain regions (Steriade, 2001; Csicsvari et al, 2003). The oscillatory frequency is nearly inversely proportional to the power in general as observed from the power spectrum (Freeman et al, 2000) This inversely proportional property of the power suggests that spatially widespread slow oscillations can modulate the local neural activity (Steriade, 2001; Csicsvari et al, 2003; Sirota et al, 2003). When the slow and fast oscillatory components interact with each other, CFC phenomena emerge
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