Coherence resonance and synchronization of Hindmarsh-Rose neurons with noise

Noise effects on coherence resonance and synchronization of Hindmarsh-Rose (HR) neuron model are studied. The coherence resonance of a single HR neuron with Gaussian white noise added to the membrane potential is investigated in situations before, near and after the Hopf bifurcation, separately, with the external direct current as a bifurcation parameter. It is shown that even though there is no coupling between neurons, uncoupled identical HR neurons driven by a common noise can achieve complete synchronization when the noise intensity is higher than a critical value. Furthermore, noise also enhances complete synchronization of weakly coupled neurons. It is concluded that synchronization in bursting neurons is easier to be induced than in spiking ones, and coupling enhances the sensitivity of synchronization of neurons to noise stimulus.     

中弧线的计算问题

已知由方程 y=f_1(x)和 y=f_2(x)给出的两条光滑的平面曲线,分别称为下型线和上型线,把与这两条型线等距离的点形成的曲线称为中弧线(见图1).显然,如果取中弧线上的任何一点 P 为圆心,都可以作一个同时与两条型线相切的圆 C,称为内切圆.内切圆与两条型线的切点分别称为下切点和上切点.中弧线的各点对应的内切圆构成内切圆族,中弧线就是内切圆族的圆心形成的曲线.     

航天动力学研究进展专辑 序

半个世纪以来,航天动力学的研究取得了较为丰硕的成果,中国航天走出了一条独立自主的发展道路,先后成功实现了“东方红一号”卫星、载人航天工程和探月工程三大里程碑的跨越．2012年6月29日,神舟九号飞船与天宫一号目标飞行器载人交会对接任务的顺利完成,标志着我国航天技术水平又向前迈进了一大步．航天器和运载火箭作为体现航天技术发展的主要载体,其研制、发射和运行是一项庞大的系统工程,而动力学分析、设计及试验验证则是航天器和运载火箭研制过程中的重要环节,动力学建模、分析方法及试验技术的正确合理性直接影响着航天器和运载火箭的设计水平,甚至决定着航天任务的成败．     

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.     

Spatiotemporal multiple coherence resonances and calcium waves in a coupled hepatocyte system

Spatiotemporal multiple coherence resonances for calcium activities induced by weak Gaussian white noise in coupled hepatocytes are studied. It is shown that bi-resonances in hepatocytes are induced by the interplay and competition between noise and coupling of cells, in other words, the cell in network can be excited either by noise or by its neighbour via gap junction which can transfer calcium ions between cells. Furthermore, the intercellular annular calcium waves induced by noise are observed, in which the wave length decreases with noise intensity augmenting but increases monotonically with coupling strength increasing. And for a fixed noise level, there is an optimal coupling strength that makes the coherence resonance reach maximum.     

第七届欧洲非线性动力学大会(ENOC 2011)简介

本文对2011年7月在意大利罗马召开的第七届欧洲非线性动力学大会(ENOC 2011)会议情况做一个简要介绍.      

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺｈａｏＪｉｅ－ｍｉｎ（赵杰民）;ＨｕａｎｇＫｅ－ｌｅｉ（黄克累）...     

Ляпунов泛函在一类反馈系统中的应用

本文通过对延迟恢复力是,外力是p(t)和摩擦与速度成比例的反馈系统构造Ляпунов泛函,获得了解的有界性、周期解的存在性和平稳振荡的存在性的容易计算、方便实用的充分条件,并获得了时滞范围的简明表达式。     

时变参数系统的非线性动力学研究

本地具有时变参数的非线性系统的摄动方法、分岔与混沌以及安全盆等问题进行综述，并简要介绍一些近期结果。     

强共振耦合Van der Pol—Duffing振子的动力学研究

本文利用数值方法研究一类非线性耦合Ｖａｎ ｄｅｒ Ｐｏｌ－Ｄｕｆｆｉｎｇ振子在强共振情形下的复杂动力学行为，分析了各参数对系统力学性态的影响，揭示了减幅、增幅、周期、拟周期和弱混沌运动等丰富现象。