IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 22, NO. 7, JULY 2011 1097 Phase Synchronization Motion and Neural Coding in Dynamic Transmission of Neural Information Rubin Wang, Zhikang Zhang, Jingyi Qu, and Jianting Cao, Member, IEEE Abstract— In order to explore the dynamic characteristics of neural coding in the transmission of neural information in the brain, a model of neural network consisting of three neuronal populations is proposed in this paper using the theory of stochastic phase dynamics. Based on the model established, the neural phase synchronization motion and neural coding under spontaneous activity and stimulation are examined, for the case of varying network structure. Our analysis shows that, under the condition of spontaneous activity, the characteristics of phase neural coding are unrelated to the number of neurons participated in neural firing within the neuronal populations. The result of numerical simulation supports the existence of sparse coding within the brain, and verifies the crucial importance of the magnitudes of the coupling coefficients in neural informa- tion processing as well as the completely different information processing capability of neural information transmission in both serial and parallel couplings. The result also testifies that under external stimulation, the bigger the number of neurons in a neu- ronal population, the more the stimulation influences the phase synchronization motion and neural coding evolution in other neu- ronal populations. We verify numerically the experimental result in neurobiology that the reduction of the coupling coefficient between neuronal populations implies the enhancement of lateral inhibition function in neural networks, with the enhancement equivalent to depressing neuronal excitability threshold. Thus, the neuronal populations tend to have a stronger reaction under the same stimulation, and more neurons get excited, leading to more neurons participating in neural coding and phase synchronization motion. Index Terms—Average number density, coupled neural net- work model, in phase neural coding, neuronal population, syn- chronized motion. I. I NTRODUCTION N EURAL information processing and neural information evolution can be studied using the theory of phase dynamics, which can describe the neural activity of a large neuronal population, reveal the dynamics of neural information processing (e.g., synchronous oscillation, dynamic coupling, rapid convergence), as well as express neuronal plasticity. Numerous reports on this topic have been published [1]–[8], [9], and many of them have been brought to the attention of Manuscript received December 13, 2010; revised February 14, 2011; accepted February 16, 2011. Date of publication June 7, 2011; date of current version July 7, 2011. This work was supported in part by the Natural Science Foundation of China under Grant 10872068 and Grant 10672057 and the Fundamental Research Funds for the Central Universities of China. The authors are with the Institute for Cognitive Neurodynamics, School of Science, School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China (e-mail: rbwang@163.com; zhikangb@163.com; qujingyi@ecust.edu.cn; cao@sit.jp). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNN.2011.2119377 neuroscientists [10]–[12]. In particular, the successful applica- tion of the theory of stochastic phase dynamics in the physical therapy of neurological diseases has aroused a lot of interest in the area of biomedicine [13]–[15]. However, the use of the theory of stochastic phase dynamics in the study of cognitive neurodynamics has a relatively short history. So far, the main contributions in this area are: 1) successful use of the description of the phase evolution of large-scale neural oscillator population in the study of attention and memory, resulting in the proposal of the neurodynamics mechanism for attention and memory, and in the analysis on the stability of attention and memory [16], [17]; 2) derivation of phase dynamic equation of the interactive neurons under stimulation, and the subsequent derivation of the model of neurodynamics of a huge neuronal population which is able to reflect the dynamics of neuronal plasticity [18]–[20]; 3) deriva- tion of the phase dynamics model of huge neural oscillator populations with time delay and consideration of inhibitory neural activity and the influence of the change of neuronal plasticity over time in the model [7], [21]; and 4) establishment of phase dynamics model of neural networks with serial coupling by multiplying the neural oscillator populations. Application of this model to the motion cognition reveals that in the spontaneous activity conditions, strong coupling will strengthen phase synchronization of neural oscillator popula- tions, while weak coupling weakens it. The following findings have been obtained through numerical simulations [22]. 1) The dynamical response of the cerebral cortex cannot encode external stimulation information. 2) The neural coding in a serial neural network system possesses the characteristic of rhythmic coding. 3) In the regulation of the nerve center system, neural inhibition plays an important role. However, the aforementioned neural network model has a serial structure, but the neural control of motion cognition actually has a neural network structure with series and parallel couplings [23], [24], [25]. This paper performs numerical sim- ulation for the phase synchronization motion of neural popula- tions and the evolution process of neural coding in neural net- works under the spontaneous motion and action of stimulation. We consider three coupling cases, namely, series and parallel coupling, series coupling and one-way coupling. Based on the model established, we attempt to tackle the following problems through numerical simulation. First, we wish to find out the differences among the three kinds of neural networks, i.e., those with serial and parallel coupling, series coupling and one-way coupling under the action of stimulation related to the 1045–9227/$26.00 © 2011 IEEE