一种最简的并行忆阻器混沌系统

在提出的一种压控忆阻器的基础上, 构造了最简的并联忆阻器混沌系统, 分析其动力学特性, 得到了该系统的Lyapunov指数和Lyapunov维数, 给出了时域波形、相图、Lyapunov指数谱、分岔图、Poincaré映射等. 利用EWB软件设计了该新混沌系统的振荡电路并进行了仿真实验. 研究结果表明, 忆阻器的i-v特性在参数的变化时, 并不保持斜“8”字形, 会变为带尾巴的扇形. 该混沌系统与磁控忆阻器混沌系统不同, 系统只有一个平衡点, 初始条件在系统能振荡的情况下不影响系统状态. 电路实验仿真结果和数值仿真具有很好的一致性, 证实了该系统的存在性和物理上可实现性. 关键词： 忆阻器 混沌电路 并联 动力学行为     

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractional-order systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.     

The simplest case of a strange attractor

It is shown that stochastic motion of strange attractor type may arise in a system with stable limit cycle if the perturbation of the system is periodical. Analytical and numerical analyses of the conditions for the strange attractor are developed.     

Elastic scattering of heavy ions — The simplest interpretation?

Elastic scattering of heavy ions with incident energies well above the Coulomb barrier is predicted from a simple extension of the Glauber theory for high energy particle-nucleus scattering. The only parameters needed are the “measured” nuclear density distribution function and the measured forward amplitude for free nucleon-nucleon scattering. An extensive comparison between theory and experiment is presented. It is demonstrated that the nuclear absorption needed to reproduce the measured differential cross section for elastic scattering can be well reproduced by means of the measured free nucleon-nucleon total cross section and the nuclear density distribution as “measured” for instance by electron scattering. Remarkable agreement between theory and experiment is demonstrated.     

A search for the simplest chaotic partial differential equation

A numerical search for the simplest chaotic partial differential equation (PDE) suggests that the Kuramoto-Sivashinsky equation is the simplest chaotic PDE with a quadratic or cubic nonlinearity and periodic boundary conditions. We define the simplicity of an equation, enumerate all autonomous equations with a single quadratic or cubic nonlinearity that are simpler than the Kuramoto-Sivashinsky equation, and then test those equations for chaos, but none appear to be chaotic. However, the search finds several chaotic, ill-posed PDEs; the simplest of these, in the discrete approximation of finitely many, coupled ordinary differential equations (ODEs), is a strikingly simple, chaotic, circulant ODE system.     

Fractals and chaotic scattering of atoms in the field of a standing light wave

Journal of Experimental and Theoretical Physics - The motion of a two-level atom with an internal degree of freedom that interacts with the field of a single-mode standing light wave in a high-Q...     

General relativistic analysis of simplest optical gravitational wave detectors

In this article we continue to study the simplest forward trip optical position meter in the frame-work of general relativity. We demonstrate the apparent paradox arising from careless analysis of these system in the laboratory reference frame (corresponding to the transeverse-traceless gauge) and show the way to overcome this problem in the proper reference frame of observer (corresponding to the local Lorentz gauge). Then we show that careful taking into account initial synchronization procedure solves this problem even in transeverse-traceless gauge.     

Noise-enhanced trapping in chaotic scattering

We show that noise enhances the trapping of trajectories in scattering systems. In fully chaotic systems, the decay rate can decrease with increasing noise due to a generic mismatch between the noiseless escape rate and the value predicted by the Liouville measure of the exit set. In Hamiltonian systems with mixed phase space we show that noise leads to a slower algebraic decay due to trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands. We argue that these noise-enhanced trapping mechanisms exist in most scattering systems and are likely to be dominant for small noise intensities, which is confirmed through a detailed investigation in the Hénon map. Our results can be tested in fluid experiments, affect the fractal Weyl's law of quantum systems, and modify the estimations of chemical reaction rates based on phase-space transition state theory.     

Quantum chaotic scattering with CsI molecules

A molecular beam of CsI molecules passed through the electric field created by a pair of charged wires is proposed as a laboratory experiment on quantum chaotic scattering. It is shown that the proposed experiment is realistic.     

Basin topology in dissipative chaotic scattering

Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that the algebraic decay of scattering particles immediately becomes exponential in the presence of weak dissipation. Here we extend the result to continuous-time Hamiltonian systems by using the Henon-Heiles system as a prototype model. More importantly, we go beyond to investigate the basin structure of scattering dynamics. A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not. We provide numerical evidence and a geometric theory for the structural stability of the complex basin topology.     

Resonance eigenfunctions in chaotic scattering systems

We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ħ → 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.     

Stimulated raman scattering in chaotic fields

Stimulated Raman scattering in chaotic fields of arbitrary band width is studied subject to the condition that the life time of the molecular vibrations is much smaller than the pump correlation time. Using the Karhunen-Loéve expansion of gaussian stochastic process, exact expressions for the intensity and the amplitude correlations of the Stokes field are obtained.