【作者】 李立；

【导师】 王江；

【作者基本信息】 天津大学 ， 检测技术与自动化装置， 2007， 硕士

【摘要】 神经细胞在中枢神经系统信息处理过程中起着关键的作用,神经细胞信息的传输体现了丰富的非线性特性。因此,耦合的多细胞网络的非线性动力学研究具有重要意义。神经作用是大量神经细胞形成网络,信息传递,交互作用的结果,细胞间的信号同步是神经系统信息传输中的关键机制,并且细胞网络的对称对信号的同步有很大的影响。本文主要研究神经元网络的同步问题,以及网络的对称对系统同步的影响。本文首先研究了两细胞耦合组成的对称系统的同步和稳定性问题,发现了在耦合参数的影响下,子系统会改变原有的状态,并与另一个子系统达到同步;由于耦合作用,单个子系统初值的改变可以引起整个系统从一种稳态到另一种稳态的跃迁。然后,本文将三细胞耦合的34种网络按其对称性,分为Z 3对称, D3对称,Z 2对称,内部Z 2对称和无对称等五类网络;按照细胞网络的组合方式以及电信息单向传递的原理,建立了各类网络的电缆模型和以FHN模型为基础的数学模型;本文在不考虑耦合强度的影响下,找到三细胞网络达到局部同步的对称条件;并给出了在各类对称网络中耦合参数所需满足的充分条件。研究结果证明了网络对称对系统同步的重要影响。通过数值仿真,证明了上述理论的正确性。更多还原

【Abstract】 Cells are believed to be the key elements in the signal processing of neural system. The transmitting of neural information exhibits nonlinear characteristics, so the dynamic performance of coupled neurons gets the main focus in the neuroscience research. Many cells coupling to form networks, transmitting information, and their interaction complete the neural work, the synchronization of coupled cells plays the main role in the process of neural information transmitting, and the symmetry of the cell network has a huge effect on the synchronization. In this paper, the network synchronization affected by symmetry is investigated.After studying the synchronization and stability of two symmetric coupled cells in this paper, it is found that, effected by the coupling parameter, one subsystem will change its former state and synchronize with the other subsystem. Because of the work of the coupling parameter, the change of the initial value of one subsystem would cause the whole system to change from one stable state to another.As for three-cell networks, they are first divided into five categories according to their symmetry: Z 3symmetry, D3 symmetry, Z 2symmetry, interior Z 2symmetry, none symmetry. According to the combination of the networks and the theory of information transmitting through one cell, the cable model and the mathematical model based on FHN model are established. The symmetric condition is found for local synchronization, independent of the coupling parameter; it also gives the sufficient condition of the coupling parameter for the kinds of networks to synchronize.The research proves the significant effect on synchronization from symmetry. The results of simulation demonstrate the validity of the theoretic analysis.更多还原