刺激下可变耦合神经振子群活动的非线性随机演化模型

考虑耦合强度随时间变化,提出在外刺激及噪声共同作用下神经振子群活动的动力学模型,并引入平均耦合对数密度作为神经振子群分布式时空编码模式.通过数值分析表明,一阶弱谐波刺激对神经振子群体编码没有显著的影响;强刺激或高阶谐波刺激加强了神经振子群的同步化活动,并增强了神经振子之间的耦合;不同频率谐波的组合刺激对神经编码的影响并不是相互独立的,而是具有某种非线性关系,且刺激强度较大的谐波主导神经编码.     

时变耦合复杂网络同步的自适应控制

应用自适应控制策略实现时变耦合复杂网络的同步。通过构造layapunov函数,证明了对于任意初始状态的时变耦合复杂动力学网络模型在相应的控制手段下总可以实现渐近同步,数值仿真证实了此控制策略的有效性。     

具有主共振耦合振子的混沌相位同步

通过引入混沌运动的相位定义分析了线性和非线性耦合参数对两个主共振子系统之间的混沌相位同步的影响．讨论了在严格1：1内共振条件下,两子系统不同步、不完全相位同步和完全相位同步之间的演化过程,揭示了不同状态相互转化与Lyapunov指数变化之间的关系,指出随着线性耦合力的增加,相位同步效应增强,然而随着非线性耦合力的增加,相位同步效应减弱．     

一类自同步时变耗散耦合网络内耦合矩阵选择方法

研究使一类时变耗散耦合复杂网络自同步的内耦合矩阵选择方法.在主稳定函数法的基础上,通过对节点变分方程系统阵的约当标准型进行分析,给出了几种适用于不同情况的内耦合矩阵选择方法,以同步速度为依据提出了较优内耦合矩阵的选择命题,并给出了相应的选择方法.最后以3个典型算例验证了所提出方法的有效性.     

耦合调和振子网络系统的联合连通同步

论文分析了耦合调和振子网络系统在联合连通网络拓扑结构下的引导-跟随同步问题.假定每个网络拓扑结构图不连通,但它们在有限时间内能够联合连通,利用代数图论,李雅普诺夫稳定性理论和La Salle不变原理,证明了该系统的同步稳定性.最后,数值模拟进一步验证了所得理论结果的正确性和有效性.     

时变耦合复杂网络的有限时间广义外部同步

研究了两个具有时变耦合矩阵的复杂动态网络的有限时间广义外部同步的问题。设计了有限时间控制器, 使两个网络能在有限时间内实现外部同步。利用微分方程的有限时间稳定性理论,得到了复杂网络实现有限时间外部同步的充分条件。为了验证所提方案的有效性,给出了仿真算例,算例验证了有限时间广义外部同步方案的有效性。     

混合突触作用下耦合时滞对模块神经元网络簇同步的影响

针对电突触耦合和化学突触耦合混合作用下含有耦合时滞的模块神经元网络,利用非线性动力学理论和数值仿真方法,探讨了耦合强度及耦合时滞对模块神经元网络簇同步特性的影响.结果发现,模块神经元网络中子网络内、子网络间的耦合强度都能促使簇放电神经元取得簇同步,但是时滞却对耦合诱导的簇同步具有显著的抑制作用.进一步的研究证实了本文所得的研究结果不依赖于子网络的数目与子网络的节点个数.需要指出的是,耦合时滞对神经元网络簇同步的抑制作用对治疗簇同步引发的一些神经性疾病(如帕金森病、癫痫等)具有一定的理论指导意义.     

模块神经元网络中耦合时滞诱导的簇同步转迁

利用Courbage-Nekorkin-Vdovin神经元构建含有耦合时滞的模块神经元网络模型,通过数值模拟研究了耦合强度及耦合时滞对模块神经元网络簇同步放电特性的影响.研究结果表明,适当大的耦合强度可以诱导模块神经元网络达到簇同步.同时,研究发现耦合时滞可以诱导模块神经元网络出现簇同步转迁,且当时滞大小约为网络中所有神经元平均振荡周期的整数倍数时,模块神经元网络的簇同步现象能够间歇性出现.此外,研究结果表明时滞诱导的簇同步转迁对子网络内的耦合强度、子网络间的连接概率具有鲁棒性.     

多个神经振子群网络的相位动力学编码

利用随机相变动力学理论研究运动认知的神经网络动力学模型．给出了感觉神经元集群、中间神经元集群和运动皮层神经元集群在耦合条件下相互作用、相位编码和数密度随时间的演化．探讨了神经网络在自发运动条件下以及在刺激条件下的神经网络动力学响应．通过数值模拟证实了（1）Walter J．Freeman提出的皮层动力学响应不能够编码外刺激信息的猜想;（2）串行的神经网络系统的神经编码具有节律编码的性质;（3）在中枢神经系统的调控中,神经抑制有其重要的作用．     

考虑树突整合效应的神经元网络的放电和同步特性

生物神经网络的同步被认为在大脑神经信息的处理过程中发挥了重要作用.本文在Hodgkin-Huxley(HH)神经元网络模型中考虑树突整合效应,得到修正后的DHH(Dendritic-integration-rule-based HH)神经元网络模型,研究了网络的放电和同步特性.首先以三个抑制性神经元构成的耦合系统为例,发现树突整合效应的加入提高了神经元的放电阈值;然后分别建立全局耦合的抑制性和兴奋性神经元网络,发现大的耦合强度能够诱导抑制性和兴奋性神经元网络达到几乎完全同步的状态,并且对神经元的放电幅值有较大的影响;更有趣的是,当树突整合系数为某一值时,抑制性神经元网络的同步达到最高,而兴奋性神经网络的同步达到最低.     

Phase noise analysis of oscillators with Sylvester representation for periodic time-varying modulus matrix by regular perturbations

Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time domain steady solutions of os- cillators are perturbed with traditional regular method; the periodic time-varying Jocobian modulus matrices are decomposed with Sylvester theorem, and on the resulting space spanned by periodic vectors, the conditions under which the os- cillator holds periodic steady states with any perturbations are analyzed. In this paper, stochastic calculus is applied to disclose the generation process of phase noise and calculate the phase jitter of the oscillator by injecting a pseudo sinusoi- dal signal in frequency domain, representing the white noise, and a δ correlation signal in time domain into the oscillator. Applying the principle of frequency modulation, we learned how the power-law and the Lorentzian spectrums are formed. Their relations and the Lorentzian spectrums of harmonics are also worked out. Based on the periodic Jacobian modulus matrix, the simple algorithms for Floquet exponents and phase noise are constructed, as well as a simple case is demonstrated. The analysis difficulties and the future directions for the phase noise of oscillators are also pointed out at the end.     

New approach for the analysis and design of negative‐resistance oscillators: Application to a quasi‐MMIC VCO

This article proposes a new approach for the analysis and design of negative‐resistance oscillators using computer‐aided engineering tools. The method presented does not require any special probe and makes the oscillator design similar to the methodology applied to amplifiers. It speeds up convergence and avoids uncertainties in the solution. The negative‐resistance oscillator is split into two parts: an active‐amplifying part and a resonator part. A chain is constructed by linking both parts and repeating them several times, which is known as the repeated circuit simulation procedure. This method allows the separation of the signal flowing between them. Small‐signal AC‐sweep and harmonic‐balance techniques, both available in several commercial software packages, are applied. This method is theoretically justified and shows convergence with less iteration. Furthermore, it is more robust than standard harmonic‐balance probes in the case of multiple frequencies of oscillation. It has been demonstrated in the design of a quasi‐MMIC VCO. This VCO has an external resonator circuit (coaxial resonator and varactor) and a MMIC negative‐resistance circuit, which was manufactured using ED02AH p‐HEMT technology (OMMIC). © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Synchronization of coupled harmonic oscillators in a dynamic proximity network

In this paper, we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network. Unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity, we show that the coupled harmonic oscillators can always be synchronized, without imposing any network connectivity assumption. Moreover, we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader, again without any assumption on connectivity of the followers. Numerical simulation illustrates the theoretical results.