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1.
同伦分析法在求解非线性演化方程中的应用   总被引:5,自引:0,他引:5       下载免费PDF全文
利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明,同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展, 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.  相似文献
2.
点电荷和介质球系统的镜像电荷分布   总被引:2,自引:0,他引:2  
用镜像法处理介质中的静电问题,一般书刊上只论及到两种情形:一是两均匀电介质交界面为一无限大平面,在其中一种介质中有一点电荷;二是无限长均匀电介质圆柱置于另一均匀介质之中,在圆柱内或圆柱外有一与其轴线平行的无限长线电荷.在这两种情形中,电势都可以用简单的镜像系表示  相似文献
3.
吸收型双光子光学双稳态的时间行为   总被引:1,自引:0,他引:1       下载免费PDF全文
汪映海  胡成生  汪志诚 《物理学报》1992,41(10):1598-1604
利用多重时间尺度微扰分析方法,研究了一个半经典吸收型双光子光学双稳系统的时间演化行为。一级近似结果表明,在高透射分支附近,系统的长时间行为由输出场振幅的方程所支配,其它动力学量除绝热地跟随场振幅变化而外,还有快速振荡。而在低透射分支附近,所有动力学变量都通过长时间尺度变化,没有与短时间尺度相联系的振荡行为。稳定态在高透射分支与低透射分支之间的跃变可以由简单的方程描述。  相似文献
4.
关剑月  吴枝喜  汪映海 《中国物理》2007,16(12):3566-3570
We investigate an evolutionary snowdrift game on a square $N=L\times L$ lattice with periodic boundary conditions, where a population of $n_{0}$ ($n_{0}\leq N$) players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability $p$ to one of the player's nearest empty sites. It is shown that, when $p=0$, the cooperative behaviour can be enhanced in disordered structures. When $p>0$, the effect of mobility on cooperation remarkably depends on the payoff parameter $r$ and the density of individuals $\rho$ ($\rho=n_{0}/N$). Compared with the results of $p=0$, for small $r$, the persistence of cooperation is enhanced at not too small values of $\rho$; whereas for large $r$, the introduction of mobility inhibits the emergence of cooperation at any $\rho<1$; for the intermediate value of $r$, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of $p$ and $\rho$. In particular, the cooperator density can reach its maximum when the values of $p$ and $\rho$ reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large $r$ in the case of $p>0$.  相似文献
5.
We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.  相似文献
6.
For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous work, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinitedimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.  相似文献
7.
We investigate a spatial Prisoner's Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α (-〉0) is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.  相似文献
8.
We study a memory-based Boolean game (MBBG) taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free parameter p between 0 and 1 is introduced to denote the strength of the agent willing to make a decision according to its memory. It is found that giving proper willing strength p, the MBBG system can spontaneously evolve to a state of performance better than the random game; while for larger p, the herd behaviour emerges to reduce the system profit. By analysing the dependence of dynamics of the system on the memory capacity M, we find that a higher memory capacity favours the emergence of the better performance state, and effectively restrains the herd behaviour, thus increases the system profit. Considering the high cost of long-time memory, the enhancement of memory capacity for restraining the herd behaviour is also discussed, and M =5 is suggested to be a good choice.  相似文献
9.
We study signal detection and transduction of dynamic neuronal systems under the influence of external noise,white and coloured. Based on simulations, we show explicitly phase locking phenomena between the output and the input of a single neuron and Electroencephalogram-like activities on neural networks with small-world connectivity. The numerical results prove that the dynamic neuronal system can be adjusted to an optimal sensitive state for signal processing in the presence of additive noise.  相似文献
10.
We study the growth of weighted networks with exponential aging of sites. Each new vertex of the network is connected to some old vertices with proportional (i) to the strength of the old vertex and (ii) to e^-αT, where T is the age of the old vertex and α is a positive constant. As soon as the preferential attachment is modified by such factors, the interesting quantities of the produced network (the vertex degree, vertex strength, clustering coefficient and average path length) will be significantly transformed.  相似文献
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