The Effect of Inhibitory Neuron on the Evolution Model of Higher-Order Coupling Neural Oscillator Population

We proposed a higher-order coupling neural network model including the inhibitory neurons and examined the dynamical evolution of average number density and phase-neural coding under the spontaneous activity and external stimulating condition. The results indicated that increase of inhibitory coupling strength will cause decrease of average number density, whereas increase of excitatory coupling strength will cause increase of stable amplitude of average number density. Whether the neural oscillator population is able to enter the new synchronous oscillation or not is determined by excitatory and inhibitory coupling strength. In the presence of external stimulation, the evolution of the average number density is dependent upon the external stimulation and the coupling term in which the dominator will determine the final evolution. 1. Introduction The quantitative analysis of the dynamics of neural oscillator population has become a highly publicized study [1, 2]. Gray and Singer found synchronous oscillations caused by external stimulus in cat primary visual cortex in 1989 [3]. Massive animal experiments suggested that the dynamics of synchronous oscillation is closely related to the message transition in the certain cortex [4]. The cerebral cortex is the unstable complicated nonlinear dynamical system. Furthermore, the nonlinear dynamics analysis method has succeeded applies in the neurodynamics research. The theory of phase transition dynamics was applied to the studies of physiological rhythms by Winfree [5] and had obtained lots of improvements by Kuramoto who described the dynamic evolution of neural oscillator population oscillation by the number density. P. A. Tass proposed theory of stochastic phase transition dynamics and further applied the theory triumphantly used to neurodegenerative disease [6–8]. Wang et al. applied stochastic dynamics of phase transformation to the research on cognitive neurodynamics and received many conclusions with actual physiological significance by means of numerical analysis and simulation [9–13]. The inhibitory neurons play an extremely important role in synchronous motion of neural oscillator populations and the evolution of neural coding [13]. Liu et al. proposed a stochastic nonlinear phase dynamic model under the coupling action of inhibitory neurons and analyzed the spontaneous behavior and the dynamic evolution of average number density under the condition of simulation. Trappenberg studied neural encoding and decoding of neural oscillator population under the strong inhibitory condition [14]. Weigenand et