The α-limit sets of a unimodal map without homtervals

Let f:I→I be a unimodal map on I without homtervals. We characterize the α-limit set of each point in I by considering the consecutive renormalization process of f.     

Logistic映射三周期轨道分支值确定

运用分支函数的方法研究了Logistic映射出现稳定三周期点的参数窗口,借助软件Singular 2.0.3运用多元多项式的Grobner基并结合严格局部分析的方法给出Logistic映射出现稳定三周期点时的参数值范围,最后数值模拟方法对所得的结果进行了验证,并指出伪轨现象.     

叶片扩压器进口安装角对离心压缩机性能影响的数值与实验研究

对不同扩压器进口安装角下离心压缩机的性能进行了实验研究,并详细计算分析了相应的流场分布。分析表明, 不同的进口安装角对压缩机的流动有较大的影响,压缩机的性能曲线也有不同程度的左右偏移;进口处较大的正冲角和负冲角均会在扩压器叶片表面出现大尺度的分离涡团;在给定的流量工况下,应存在一个最佳的进口安装角,使得扩压器效率最高;设计工况下,最高效率所对应的冲角并非为零。     

耦合映像格子中时空混沌的状态反馈控制

利用状态反馈的方法，实现了耦合映像格子中时空混沌的稳定控制.反馈方式可以是没有延迟的，也可以是有延迟的；控制方式可以是连续的，也可以是脉冲的.数值模拟结果证明了状态反馈方法的有效性. 关键词： 耦合映像格子 时空混沌 状态反馈控制     

单向耦合映象格子的时空混沌同步

以耦合映象格子为对象,研究了时空混沌系统的同步问题. 基于Lyapunov稳定性定理,通过恰当地选择驱动函数,实现了两个单向耦合映象格子的完全同步. 仿真模拟验证了这种同步方法的有效性. 讨论了控制参量对同步速率的影响. 仿真模拟还表明,在存在系统偏差并受到噪声影响的情况下,仍然可以实现两系统的同步,这种同步方法具有一定的抗干扰能力. 关键词： 时空混沌 同步 耦合映象格子     

Hash function based on the generalized Henon map

A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map, and use it to construct Hash function. First we divide the message into groups, and then carry out the Xor operation between the ASCII value of each group and the binary sequence, the result can be used as the initial values of the next loop. Repeat the procedure until all the groups have been processed, and the final binary sequence is the Hash value. In the scheme, the initial values of the generalized Henon map are used as the secret key and the messages are mapped to Hash values with a designated length. Simulation results show that the proposed scheme has strong diffusion and confusion capability, good collision resistance, large key space, extreme sensitivity to message and secret key, and it is easy to be realized and extended.     

Probabilistic signatures of spatiotemporal intermittency in the coupled sine circle map lattice

The phase diagram of the coupled sine circle map system exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures termed solitons. A spreading to non-spreading transition is seen in the system. A cellular automaton version of the coupled system maps the spreading to non-spreading transition to a transition from a probabilistic to a deterministic cellular automaton. The solitonic sector of the system shows spatiotemporal intermittency with soliton creation, propagation and absorption. A probabilistic cellular automaton mapping is set up for this sector which can identify each one of these phenomena.      

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

The dynamical feature of transition of a Hamiltonian system to a dissipative system

The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formation of attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.