A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping

We put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of discrete maps. The resulting transfer measure possesses a property of directionality or transfer asymmetry as emphasized by Schreiber [T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85 (2) (2000) 461]; it also verifies the transfer measure for two-dimensional systems, which was obtained by Liang and Kleeman [X.S. Liang, R. Kleeman, Information transfer between dynamical system components, Phys. Rev. Lett. 95 (24) (2005) 244101] through a different avenue. Connections to classical formalisms are explored and applications presented. We find that, in the context of the baker transformation, there is always information flowing from the stretching direction to the folding direction, while no transfer occurs in the opposite direction; we also find that, within the Hénon map system, the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds. This latter result is unique to our formalism.     

Information entropy of a dynamical system driven by quasimonochromatic noise

This paper shows the Fokker-Planck equation of a dynamical system driven by quasimonochromatic noise. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production for the system is calculated. The relationship between the properties of quasimonochromatic noise and dissipative parameter and their effects on entropy flux and entropy production are discussed.     

Principal components of the protein dynamical transition

Proteins exhibit a solvent-driven dynamical transition at 180-220 K, manifested by nonlinearity in the temperature dependence of the average mean-square displacement. Here, molecular dynamics simulations of hydrated myoglobin show that the onset of the transition at approximately 180 K is characterized by the appearance of a single double-well principal component mode involving a global motion of two groups of helices. As the temperature is raised a few more quasiharmonic and multiminimum components successively appear. The results indicate an underlying simplicity in the protein dynamical transition.     

Excitation transfer between components of molecular layers of cyanine compounds

Using the example of layers of symmetric polymethine dyes, we have studied the optical excitation energy transfer processes between nanocomponents of a molecular layer. The fluorescence yields and life-times of excited states of monomeric stereoisomers have been estimated, and the stereoisomerization yields have been determined. We show that the excitation transfer yield between the S ₁ states of monomeric stereoisomers (tens of percent) is considerably higher than the fluorescence yield (several percent) and depends on the structure of terminal groups of the molecule.     

Wavelet analysis and Arnold web picture for detecting energy transfer in a Hamiltonian dynamical system

Our motivation is to understand how, in chemical reactions, the reaction coordinate effectively gains dynamical energy from the other degrees of freedom (i.e., bath coordinates) avoiding thermalization of the redistributed energy. In such a system, the phase space structure should be not homogeneous; i.e., the system is never ergodic. In this study, we introduce a way to capture the inhomogeneity of the phase space and to monitor energy transfers among their partial degrees of freedom in nonergodic systems using wavelet analysis and a picture of the Arnold web. First, we examine several simple energy transfer processes, i.e., a motion on a resonance line, between resonance lines, and around a resonance junction in a simple three-degree-of-freedom (DOF) system and show how the elemental processes of the intramolecular vibrational energy redistribution (IVR) are detected by our tools. We especially note that the structure of the higher order resonance of the system can be detected by wavelet analysis and motion in the action space. Next, we analyze a reaction process in a simple Hamiltonian system of 3 DOF with a double-well potential, i.e., a system with a transition state of the center-saddle-center type, and detect energy transfers in the reactive process. The aim of the study is to propose a way to characterize the inhomogeneity of the phase space, e.g., the reactive doorway, which leads to controllability of the chemical reaction by light, i.e., control of the reaction by selectively preparing an initial state in the reactive doorway by optical excitation.     

A new hyperchaotic dynamical system

In this paper a new hyperchaotic system is reported. Some basic dynamical properties, such as continuous spectrum, Lyapunov exponents, fractal dimensions, strange attractor and Poincar\'{e} mapping of the new hyperchaotic system are studied. Dynamical behaviours of the new hyperchaotic system are proved by not only numerical simulation and brief theoretical analysis but also an electronic circuit experiment.     

Quantum dynamical system with hyperbolic instabilities

An analysis of a quantum counterpart of a parametrically kicked nonlinear oscillator is given. The method, using as a basic criterion the recently introduced quantum characteristic exponents, is analogous to the technique developed in classical dynamical system theory. However, our approach to the characterization of the stability of an observable's evolution is done in pure quantum terms.     

Entropy of a fibered dynamical system

The entropy of the geodesic flow associated to a fibered dynamical system is shown to be zero; in particular the entropy of a quantizable dynamical system is zero. An ergodic dynamical system which defines a quantizable dynamical system is outlined.This research was supported in part by NSF GP-20856 A 1     

Continuum spin system as an exactly solvable dynamical system

The continuum limit of a one-dimensional classical spins with nearest neighbour Heisenberg interaction is shown to be an exactly solvable system and that its dynamics describable by the nonlinear Schrödinger equation. N-soliton solutions for the energy density exist.     

Partial dynamical symmetry in a fermion system

The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell model of nuclei and shown to be closely related to the quadrupole-quadrupole interaction. Implications are discussed for the deformed light nucleus 20Ne.     

Chaotic attractors of an infinite-dimensional dynamical system

We study the chaotic attractors of a delay differential equation. The dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of Lyapunov exponents according to a conjecture of Kaplan and Yorke. Assuming this conjecture to be valid, as the delay parameter is varied, from computations of the spectrum of Lyapunov exponents, we observe a roughly linear increase from two to twenty in the dimension, while the metric entropy remains roughly constant. These results are compared to a linear analysis, and the asymptotic behavior of the Lyapunov exponents is derived.     

On gradient dynamical system on semi-Riemannian manifolds

We consider gradient dynamical systems on a semi-Riemannian manifold of arbitrary index. The main point of the paper is the introduction of the concepts causality subsets, causality function and sector stability. As a main application we provide conditions assuring, that the nonwandering points are precisely the singular points of the gradient field. Furthermore we show, that every nonconstant recurrent orbit for the gradient field must intersect one of the causality subsets and that the stable and unstable manifolds belonging to a hyperbolic singular point for the gradient field are orthogonal.     

The simple relation between certain dynamical systems

A simple relation between certain dynamical systems is established.     

基于Matlab的非线性动力学系统分析

利用Matlab软件对洛仑兹和达芬2个典型的非线性动力学系统进行了较为详细的分析．在使学生初步掌握了如何使用Matlab软件解决数值分析中的一些计算问题和绘图问题的同时．也使学生对非线性动力学系统的运动本质有一定的认识．     

Power spectral analysis of a dynamical system

Power spectra for chaotic transitions in three dimensions are presented for a dynamical system first proposed by Rössler. Relations between the spectra and the topology of the corresponding strange attractor are discussed.     

A simple dynamical system with stochastic behaviour

The paper treats a dynamical system consisting of two quasiharmonic limit cycles cut off by stall lines. A phase trajectory inside a cycle jumps infinitely quickly to another cycle after having reached the stall line. This dynamical system can be interpreted as an asymptotical form of a system of three differential equations admitting separation of fast and slow motions. The explicit conditions on parameters of the system providing its stochastic behaviour, i.e. local instability of all trajectories, are obtained by means of investigation of the Poincaré mapping. A lower estimate for the topological entropy of the system is also obtained. The appendix concerns investigation of some properties of a system consisting of stochastic oscillators of the most simple kind connected by diffusion.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

动态银行网络系统中系统性风险定量计算方法研究

采用复杂网络理论研究银行网络系统中的系统性风险问题已有较多的报道.这些研究大多假设银行网络系统是静态的(银行节点是静态的,银行节点间的借贷关系也是静态的),然后在系统性风险已经累积到爆发的情况下,研究风险爆发后,风险在静态网络系统中的传染与网络结构的关系.然而对于系统性风险如何在银行网络中累积直至爆发的问题的研究还很少.系统风险的累积过程需在动态演化的银行网络系统中才能实现,同时观察风险累积过程需对系统风险进行定量估算.因此,本文首先建立带有宏观经济趋势及多期清算的动态银行网络系统模型;提出系统风险的定量计算方法;最后对系统风险进行仿真计算与分析,得到了系统风险变化曲线,显示了系统风险累积的过程.该研究为定量研究动态银行网络系统的风险累积问题奠定了基础.     

Investigation of element distribution between components of a salt-lake system by SR-XRF

Numerous bitter lakes, largely closed and shallow, are concentrated in a small area of the South of Western Siberia (Kulunda and Barabinsk steppes). Most lakes are marked by the development of thick black or grayish blue silt organogenic sediments formed due to the dying-off of local halophilic organisms. Salt lakes are of great interest for scientists. The investigation was conducted in the context of complex biological and biochemical studies aimed at identifying regularities in the redistribution of elements between components of a salt-lake system by SR-XRF (Synchrotron Radiation X-ray Fluorescence).