多体系统动力学方程违约修正的数值计算方法

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大.本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式.通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法.     

Information Transmitting and Cognition with a Spiking Neural Network Model

Information encoding plays a crucial role in neuroscience. One of the fundamental questions in cognitive neuroscience is how the brain encodes external stimuli in the sensory cortex. We use a network model based on the Hodgkin–Huxley type to study the information transmitting including its storage and recall. The model is inspired by psychological and neurobiological evidence on sequential memories. The model contains excitatory and inhibitory neurons with all-to-all connections whose architecture has two layers. A lower layer represents consecutive events during the information encoding process, and the upper layer is used to tag sequences of events represented in the lower layer. The spike-timing-dependent plasticity learning rule is used for sequential storage of excitatory connections between the modules. Computer simulations demonstrate that the synchronization status of multiple neurons is dependent on the network connectivity patterns, and also this model has good performance for different sequences of storage and recall.     

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated.The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach.Based on Lyapunov’s stability theory,linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H∞-norm constraint.Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems.Numerical simulations are also given to identify theeffectiveness of the theoretical analysis.     

连续自映射及其扭扩半流的不变测度

本文研究了紧致度量空间上连续自映射及连续半流的不变测度,并且证明了如下结论(1)在拓扑等价的无不动点的连续半流的不变测度之间以及在连续自映射及其扭扩半流的不变测度之间存在一一对应;(2)作为(1)的应用,给出如下结论(见[2,定理2.1])"环面上无不动点的连续流是唯一遍历的当且仅当它至多有一条周期轨"一个易接受的证明.     

连续自映射及其扭扩半流的不变测度

本文研究了紧致度量空间上连续自映射及连续半流的不变测度,并且证明了如下结论:(1)在拓扑等价的无不动点的连续半流的不变测度之间以及在连续自映射及其扭扩半流的不变测度之间存在一一对应;(2)作为(1)的应用,给出如下结论(见[2,定理2.1]):“环面上无不动点的连续流是唯一遍历的当且仅当它至多有一条周期轨”一个易接受的证明.     

具有非线性控制的Chua电路的混沌同步

Chua电路是一个非光滑系统.本文通过广义哈密顿系统和观测器方法,将具有非线性控制的Chua电路的混沌同步问题转化成研究具有非线性控制的光滑系统的零解稳定性;进而利用滑模控制对该光滑系统的零解稳定性进行了研究,从而使得Chua电路达到了混沌同步.最后,将上述方法应用到具体系统,数值结果也表明其正确性.