一类永磁同步电动机混沌模型与霍夫分叉

从基于d-q轴永磁同步电动机模型出发,应用时间尺度变换和线性仿射变换,建立了一个适用于永磁同步电动机混沌运动分析的模型,在研究永磁同步电动机同步速附近运动条件下,得到一个三阶的非线性自治方程。利用该方程,根据李雅普诺夫稳定性分析理论,针对不同外部输入电压状况对其出现霍夫分叉的条件及稳定性进行了分析,研究表明,当均匀气隙永磁同步电动机参数确定情况下,在一定输入电压范围内,它将在同步速附近产生不稳定的霍夫分叉运动,并进入混沌状态和产生奇怪吸引子,计算机仿真展现了这一过程。     

Genes without prominence: a reappraisal of the foundations of biology

The sequencing of the human genome raises two intriguing questions: why has the prediction of the inheritance of common diseases from the presence of abnormal alleles proved so unrewarding in most cases and how can some 25 000 genes generate such a rich complexity evident in the human phenotype? It is proposed that light can be shed on these questions by viewing evolution and organisms as natural processes contingent on the second law of thermodynamics, equivalent to the principle of least action in its original form. Consequently, natural selection acts on variation in any mechanism that consumes energy from the environment rather than on genetic variation. According to this tenet cellular phenotype, represented by a minimum free energy attractor state comprising active gene products, has a causal role in giving rise, by a self-similar process of cell-to-cell interaction, to morphology and functionality in organisms, which, in turn, by a self-similar process entailing Darwin''s proportional numbers are influencing their ecosystems. Thus, genes are merely a means of specifying polypeptides: those that serve free energy consumption in a given surroundings contribute to cellular phenotype as determined by the phenotype. In such natural processes, everything depends on everything else, and phenotypes are emergent properties of their systems.     

An artificial neural network noise reduction method for chaotic attractors

A method is presented to reduce noise in chaotic attractors without knowing the underlying maps. The method is based on using Artificial Neural Network (ANN) for moderate levels of additive noise. For high levels of additive noise, a combination of a refinement procedure with ANN is used. In this case, only one refinement is needed for the successful use of ANN. The obtained ANN model is used for long-term predictions of the future behavior of a Henon attractor, using information based only on past values.     

On Ilyashenko’s statistical attractors

We define a minimal α-observability of Ilyashenko’s statistical attractors. We prove that the space is always full Lebesgue decomposable into pairwise disjoint sets that are Lebesgue-bounded away from zero and included in the basins of a finite family of minimal α-observable statistical attractors. Among other examples, we analyse the Bowen homeomorphisms with non-robust topological heteroclinic cycles. We prove the existence of three types of statistical behaviours for these examples.     

Synchronization of chaotic attractors with different equilibrium points

This paper investigates the synchronization of coupled chaotic systems with many equilibrium points. By addition of an external switching piecewise-constant controller, the system changes to a new one with several independent chaotic attractors in the state space. Then, by addition of a nonlinear state feedback control, the chaos synchronization is presented. This method can be used in many couples of chaotic systems characterized by the same equilibrium point or by two different equilibrium points, even they are the same systems (Lorenz, Jerk, Van der Pol) or two chaotic systems with different structures (Lorenz modified).     

Left invertibility of discrete systems with finite inputs and quantised output

The aim of this article is to address left invertibility for dynamical systems with inputs and outputs in discrete sets. We study systems which evolve in discrete time within a continuous state-space. Quantised outputs are generated by the system according to a given partition of the state-space, while inputs are arbitrary sequences of symbols in a finite alphabet, which are associated to specific actions on the system. Our main results are obtained under some contractivity hypotheses. The problem of left invertibility, i.e. recovering an unknown input sequence from the knowledge of the corresponding output string, is addressed using the theory of iterated function systems (IFS), a tool developed for the study of fractals. We show how the IFS naturally associated to a system and the geometric properties of its attractor are linked to the invertibility property of the system. Our main result is a necessary and sufficient condition for left invertibility and uniform left invertibility for joint contractive systems. In addition, an algorithm is proposed to recover inputs from output strings. A few examples are presented to illustrate the application of the proposed method.     

基于虚拟仪器三维四翼混沌系统研究及实现

讨论了基于虚拟仪器三维四翼混沌系统的研究模式,设计了软件系统,并给出三维四翼混沌系统电路原理图及其实验结果,证实基于虚拟仪器技术为研究非线性系统提供可行的方案,利用此方案进行实验,结果证明此实验系统具有良好的实验效果。与传统的自治混沌系统相比,此系统具有参数调节方便、易实现、可靠性高,实时性好等优点,该特点在保密通信等工程中有重要的应用。     

含无损传输线的约瑟夫森结电磁系统中的分岔与混沌

 建立了含无损传输线的约瑟夫森结电磁系统左端点处电压正向行波分量的一维Poincaré映射模型,运用非线性动力学理论分析了映射定点的稳定性。通过数值计算得到了映射随电压反射系数变化的分岔图,详细分析了系统随参数变化的动态演化过程。结果表明在一定参数条件下,该电磁系统中存在着分岔、混沌、周期吸引子共存、混沌吸引子共存以及周期与混沌吸引子共存等复杂的非线性动力学行为。     

Chaos in mechanical systems — A review

In this paper, a review of the various developments in the field of chaotic dynamics with specific emphasis on chaos in structural and mechanical systems is presented. The paper discusses some known chaotic systems such as the Lorenz, Rössler, Ueda and Henon attractors as well as chaos in Duffing and Van der Pol oscillators. The paper also covers chaos in piecewise linear systems, impacting oscillators and flow induced vibrating systems. Topics such as bifurcations and routes to chaos, different ways of characterising chaos, domains of attraction and control of chaos are also discussed.