Wada basins of strange nonchaotic attractors in a quasiperiodically forced system

Whether Wada basins of strange nonchaotic attractors (SNAs) can exist has been an open problem. Here we verify the existence of Wada basin for SNAs in a quasiperiodically forced Duffing map. We show that the SNAs? basins are full Wada for a set of parameters of positive measure. We identify two types of SNAs? Wada basins by the basin cell method. It suggests that SNAs cannot be predicted reliably for the specific initial conditions.     

Wada bifurcations and partially Wada basin boundaries in a two-dimensional cubic map

The partially Wada basin boundaries are referred to the coexistence of Wada points and non-Wada points in the same basin boundary. We demonstrate two types of Wada bifurcations and analyze the transitions from totally Wada basins to partially Wada basins and from totally Wada basins to totally Wada basins in a two-dimensional cubic map. We describe some numerical experiments giving the evidence of partially Wada basin boundaries. Our results show that the basin cell erosion and the basin cell bifurcation can induce the Wada basin boundary metamorphoses.     

A plethora of strange nonchaotic attractors

We show that it is possible to devise a large class of skew-product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is non-positive. Furthermore, we show that quasiperiodic forcing, which has been a hallmark of essentially all hitherto known examples of such dynamics is not necessary for the creation of SNAs.     

A special type of explosion of basin boundary

We study a special type of explosion of a basin boundary set in an archetypal oscillator. A typical feature is that the basin boundaries change the number of basins separating at the same time. Before the explosion, a basin boundary contains some Wada points of ten basins. After the explosion, the basin boundary contains some Wada points of eighteen basins. The underlying mechanism for the explosion is investigated by the heteroclinic tangency and Lambda lemma. Basin entropy and boundary basin entropy are also used to describe the nature of basins of attraction and the basin boundary explosion.     

Study of the Wada fractal boundary and indeterminate crisis

By using the generalized cell mapping digraph (GCMD)method,we study bifurcations governing the escape of periodically forced oscillators in a potential well,in which a chaotic saddle plays an extremely important role.Int this paper,we find the chaotic saddle,and we demonstrate that the chaotic saddle is embedded in a strange fractal boundary which has the Wada property,that any point on the boundary of that basin is also simultaneously on the boundary of at least two other basins.The chaotic saddle in the Wada fractal boundary,by colliding with a chaotic attractor,leads to a chaotic boundary crisis with a global indeterminate outcome which presents an extreme form of indeterminacy in a dynamical system.We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary particularly concentrating on its discontinuous bifurcations(metamorphoses),We demonstrate that the chaotic saddle in the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal boundaries.After a final escape bifurcation,there only exists the attractor at infinity;a chaotic saddle with a beautiful pattern is left behind in phase space.     

基于时变耦合映像格子模型的信号初值估计

从耦合映像格子中,恢复系统初始条件是耦合系统求逆问题,也是信号处理研究中的一个关键性问题.本文在符号动力学方法的基础上,对映像系数进行修正,针对耦合单峰Logistic映射,提出一种基于时变映像系数恢复信号初值的新方法.在映像过程无噪或受到高斯白噪声污染时,本文方法都能够较好地恢复信号初值的统计特性,而且具有较小的偏差和均方误差,并与原信号之间具有较强的相关性,从而能够更好和更加合理地刻画实际信号的物理过程,对系统初值做出更优的估计. 关键词： 耦合映像格子 恢复初值的统计特性 时变映像系数     

A seven-mode truncation of the plane incompressible Navier-Stokes equations

A model obtained by a seven-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is studied. This model, extending a previously studied five-mode one, exhibits a very rich and varied phenomenology including some remarkable properties of hysteresis (i.e., coexistence of attractors). A stochastic behavior is found for high values of the Reynolds number, when no stable fixed points, closed orbits, or tori are present.     

Four-dimensional parameter estimation of plane waves using swarming intelligence

This paper proposes an efficient approach for four-dimensional(4D) parameter estimation of plane waves impinging on a 2-L shape array. The 4D parameters include amplitude, frequency and the two-dimensional(2D) direction of arrival,namely, azimuth and elevation angles. The proposed approach is based on memetic computation, in which the global optimizer, particle swarm optimization is hybridized with a rapid local search technique, pattern search. For this purpose,a new multi-objective fitness function is used. This fitness function is the combination of mean square error and the correlation between the normalized desired and estimated vectors. The proposed hybrid scheme is not only compared with individual performances of particle swarm optimization and pattern search, but also with the performance of the hybrid genetic algorithm and that of the traditional approach. A large number of Monte–Carlo simulations are carried out to validate the performance of the proposed scheme. It gives promising results in terms of estimation accuracy, convergence rate, proximity effect and robustness against noise.     

超混沌吸引子的翼倍增方案

通过对一个五维超混沌系统施加平移变换、镜像映射和滞回切换操作,将多翼混沌吸引子结构由双翼倍增为四翼.施加n-1次相似操作可以得到2ⁿ翼的超混沌吸引子.设计了一个简单的电路实现吸引子翼数量的倍增.该方法在保留了系统原有超混沌特性的基础上,增加了吸引子的拓扑结构复杂性,使之更适合保密通信等领域的应用. 关键词： 多涡卷吸引子 多翼吸引子 超混沌系统     

Statistics of strange attractors by generalized cell mapping

It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.     

橡皮筋滞后特性的实验分析

利用约利弹簧秤对橡皮筋的力的滞后特性进行了实验分析，并由此说明了不能用橡皮筋做测力计的物理机理，为检验弹簧的质量提供了一种实验途径及理论依据．     

Strange stars properties calculated in the framework of the Field Correlator Method

We calculate the strange star properties in the framework of the Field Correlator Method. We find that for gluon condensate values G₂$G_2$ in the range 0.006–0.007 GeV⁴$0.006\text{–}0.007{\text{GeV}}^4$, which give a critical temperature Tc∼170 MeV$T_c\sim 170\text{MeV}$ at μc=0${\mu }_c=0$, the sequences of strange stars are compatible with some of the semi-empirical mass–radius relations and data obtained from astrophysical observations.     

Computation of the largest Lyapunov exponent by the generalized cell mapping

The method of cell mappings has been developed as an efficient tool for the global study of dynamical systems. One of them, the generalized cell mapping (GCM), describes the behavior of a system in a probabilistic sense, and is essentially a Markov chain analysis of dynamical systems. Since the largest Lyapunov exponent is widely used to characterize attractors of dynamical systems, we propose an algorithm for that quantity by the GCM. This allows us to examine the persistent groups of the GCM in terms of their Lyapunov exponent, thereby connecting them with their counterparts in point mapping systems.     

溶胶-凝胶VO2薄膜转换特性研究

利用溶胶凝胶法在SiO2Si衬底上沉积高取向的V2O5薄膜,在压强低于2Pa,温度高于400℃的条件下,对V2O5薄膜进行真空烘烤,获得了电阻率变化3个数量级以上、弛豫宽度为62℃的VO2多晶薄膜.以X射线衍射(XRD)、扫描电子显微镜(SEM)图和电阻率转换特性等实验结果为依据,详细分析了溶胶凝胶薄膜在真空烘烤时从V2O5向VO2的转化,它经历了从VnO2n+1(n=2,3,4,6)到VO2的过程.实验证明,根据选择合适的成膜热处理条件和真空烘烤条件是实现溶胶凝胶V2O5结构向VO2结构成功转换的关键 关键词： 溶胶-凝胶法 氧化钒薄膜 VO2膜转换特性     

FLAPW方法研究δ-钚(001)面的性质

采用 FLAPW(全势线性缀加平面波)方法,在广义梯度近似(GGA)、反铁磁(AFM)下研究了δ-钚(001)面的性质.计算得到的表面能系数和功函数分别为0.08 eV/(A)2和3.15 eV,接近其近邻元素α-铀的实验值(0.094 eV/(A)2和3.4～3.9 eV).与体相原子相比,表层原子由于近邻原子数目的减少,5f-5f和5f-6d轨道波函数重叠、杂化几率降低,5f电子定域化特性增强,局部磁矩增大.表层原子向内收缩2.70%,然而,由于表面弛豫能很小,δ-钚(001)面相当稳定.     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

Decay of amplitude-modulation property of song and an analysis of sounding mechanism in mottled cicade (Gaeana maculata Drury)

I-IntroductionTheamp1itudc-modulationpropcrtyexistsgcnerallyinthesongsofarthropods.Insingingorthoptcraninsccts,suchasmo1c-cricket,1ocust,cricketandkatydid,thesongsproduccdbystridulationsarctypica1andcachwave(thetoothstrike)incarrierwavesisisproducedbythatthescrapcrstrikesateachtoothofthedenticulatedvein(fi1e)t'J.IncicadasoftheHomoptera,thesongsareproduccdbycontractionmovcmentsofthesoundingmusc1etodrivethesoundingmembranewithribstructurestovibrations,andaregeneral1yamplitude-modu1ationpu1sesou…     

Effects of pre-deformation on the martensitic transformation and magnetocaloric property in Ni-Mn-Co-Sn ribbons

This paper investigates the martensitic transformation and magnetocaloric effect in pre-deformed Ni-Mn-Co-Sn ribbons.The experimental results show that the reverse martensitic transformation temperature T M increases with the increasing pre-pressure,suggesting that pre-deformation is another effective way to adjust T M in ferromagnetic shape memory alloys.Large magnetic entropy changes and refrigerant capacities are obtained in these ribbons as well.It also discusses the origin of the enhanced martensitic transformation temperature and magnetocaloric property in pre-deformed Ni-Mn-Co-Sn ribbons.     

Conversion of a chaotic attractor into a strange nonchaotic attractor in an one dimensional map and BVP oscillator

In this paper we investigate numerically the possibility of conversion of a chaotic attractor into a nonchaotic but strange attractor in both a discrete system (an one dimensional map) and in a continuous dynamical system — Bonhoeffer—van der Pol oscillator. In these systems we show suppression of chaotic property, namely, the sensitive dependence on initial states, by adding appropriate i) chaotic signal and ii) Gaussian white noise. The controlled orbit is found to be strange but nonchaotic with largest Lyapunov exponent negative and noninteger correlation dimension. Return map and power spectrum are also used to characterize the strange nonchaotic attractor.