Oscillatory Resonance and Dynamic Manifolds in Cortical Networks With Time Delay and Multiple External Stimuli

Abstract

Rhythmic oscillation is crucial for information transmission and neural communication among different brain areas. Stochastic resonance (SR) can evoke different patterns of neural oscillation. However, the characteristics of network resonance and underlying dynamical mechanisms are still unclear. In this paper, a biological model of cortical network is established and its dynamical response to external periodic stimulation is investigated. We explore the oscillatory resonance of excitatory and inhibitory populations in cortical network. It is found that the intrinsic parameters of neural populations determine the extent of resonant activity, indicating that the firing rate exhibits coherent oscillation when the frequency of external stimulation is close to intrinsic frequency of neural population. In addition, the nonlinear dynamics of cortical network in oscillatory resonance can be represented by helical manifolds in low-dimensional state space. The geometry of neural manifolds reveals the periodic dynamics and state transition in oscillatory resonance. Moreover, time delay in chemical synapses can induce multiple resonances, which appear intermittently at integer multiples of the period of input signal. The dynamical response of neural population achieves maximal periodically, due to the transition of network states induced by time delay. Furthermore, mean-field theory is applied to analyze theoretical dynamic of cortical networks with time delay and demonstrate the effective transmission of stimulation information via oscillatory resonance in the brain. Consequently, the obtained results contribute to the improvement of neuromodulation for neurological disease from the viewpoint of the neural basis.

Keywords

• Oscillatory resonance
• cortical network
• neural manifold
• time delay
• neuromodulation mechanism