单神经元自适应PID控制器的研究

将二次型性能指标引入单神经元并利用自学习功能构成了自适应ＰＩＤ控制器;分析了神经元自适应控制系统的稳定性和学习算法的收敛性。仿真结果表明,这种控制方案具有良好的自适应性。     

化学突触耦合神经元的簇放电同步

本文研究了经化学突触耦合的两个神经元的簇放电同步以及耦合后神经元的簇放电动力学性质.根据簇相位的定义,通过计算得到兴奋性耦合导致两个神经元达到同相簇放电同步,而抑制性耦合则使得两个神经元反相同步产生簇放电.本文给出了衡量单个神经元簇动力学的指标-宽度因子,根据此指标将簇放电模式分类为短簇和长簇两种,并且讨论了不同簇放电模式以及耦合方式对于耦合后神经元簇动力学性质的影响.结果表明兴奋性耦合有利于簇放电的整合,短簇的放电模式对于耦合作用具有鲁棒性.这一结果的研究对于将来神经实验中识别簇放电同步具有指导意义.     

Nonlinear neural networks. I. General theory

A neural network is called nonlinear if the introduction of new data into the synaptic efficacies has to be performed through anonlinear operation. The original Hopfield model is linear, whereas, for instance, clipped synapses constitute a nonlinear model. Here a general theory is presented to obtain the statistical mechanics of a neural network with finitely many patterns and arbitrary (symmetric) nonlinearity. The problem is reduced to minimizing a free energy functional over all solutions of a fixed-point equation with synaptic kernelQ. The case of clipped synapses with bimodal and Gaussian probability distribution is analyzed in detail. To this end, a simple theory is developed that gives the spectrum ofQ and thereby all the solutions that bifurcate from the high-temperature phase.     

Cluster synchronization and rhythm dynamics in a complex neuronal network with chemical synapses

Cluster synchronization and rhythm dynamics are studied for a complex neuronal network with the small world structure connected by chemical synapses. Cluster synchronization is considered as that in-phase burst synchronization occurs inside each group of the network but diversity may take place among different groups. It is found that both one-cluster and multi-cluster synchronization may exist for chemically excitatory coupled neuronal networks, however, only multi-cluster synchronization can be achieved for chemically inhibitory coupled neuronal networks. The rhythm dynamics of bursting neurons can be described by a quantitative characteristic, the width factor. We also study the effects of coupling schemes, the intrinsic property of neurons and the network topology on the rhythm dynamics of the small world neuronal network. It is shown that the short bursting type is robust with respect to the coupling strength and the coupling scheme. As for the network topology, more links can only change the type of long bursting neurons, and short bursting neurons are also robust to the link numbers.