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1.
Chenguang Ma 《中国物理 B》2021,30(12):120504-120504
A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.  相似文献   
2.
王校锋  司守奎  史国荣 《物理学报》2006,55(11):5694-5699
提出了混沌同步有限时间实现问题,将Terminal滑模控制技术与混沌同步问题相结合,把同步问题视为响应系统的跟踪问题,给出了由线性滑模函数引入非线性项构造Terminal滑模面的充分条件,以及相应Terminal滑模控制器.以主从Duffing系统为例研究验证同步策略的可行性和有效性. 关键词: Terminal滑模 混沌同步 Duffing系统  相似文献   
3.
王玲桃  马西奎  邹建龙  杨梅 《物理学报》2006,55(11):5657-5666
对于一个由线性无损传输线加非线性边界条件组成的简单无穷维电磁系统,应用行波理论确定了电压反射波的局部映射关系.数值仿真结果表明,当系统参数发生变化时,传输线沿线电压存在着非常丰富的时空非线性现象.通过描绘出空间振幅变化图和时空行为发展图,定性分析了传输线沿线电压的时空混沌图案动态,为研究和理解时空混沌提供了一种良好的可求解模型. 关键词: 图案 时空混沌 无穷维系统 时延范德波尔电磁系统  相似文献   
4.
We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.  相似文献   
5.
苗明川  唐芳  张淼  胡涛 《大学物理》2006,25(2):53-57
大学物理实验中混沌实验大多采用观察现象的方法进行,本实验采用蔡氏电路(Chua s circuit)产生混沌行为.在观察不同初始值条件下出现的倍周期分岔、阵发混沌、奇异吸引子等相图及现象的基础上,通过对采集数据进行处理,对负电阻伏安特性进行分段线性拟合,用功率频谱法、计算机仿真方法(龙格-库塔数值积分法)对混沌现象进行描绘,将实验数据与非线性方程组的数值解相结合,呈现出混沌现象的本质.  相似文献   
6.
用自适应脉冲微扰引导混沌系统到周期解   总被引:5,自引:0,他引:5       下载免费PDF全文
张荣  徐振源 《物理学报》2006,55(10):5070-5076
用自适应脉冲微扰方法控制的系统的某个系统变量作为驱动,设计了一种自适应控制器方法对两个或多个响应混沌系统进行脉冲微扰,引导这些系统从混沌运动到低周期运动,实现同时控制多个混沌系统到不同的周期态. 当选择相同的自适应控制器输入变量实施脉冲微扰时,还可控制两个或多个混沌系统达到不同的周期态同步. 通过对R?ssler混沌系统的仿真研究证实了方法的有效性. 关键词: 混沌控制 系统参量 自适应控制器 脉冲微扰 周期态同步  相似文献   
7.
It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at  相似文献   
8.
We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning |δ|1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of |δ| to be equal to |αp0|, is found numerically and described analytically (with α to be the normalized recoil frequency and p0 the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion zout, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion zin that the probability of detecting any value of zout in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.  相似文献   
9.
We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO3 crystals we consider the cases of nonlocal (diffusive) response (BaTiO3, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003  相似文献   
10.
The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.  相似文献   
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