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。     

Response of a barrier estuary to climate change and river regulation using attractor analysis: Snowy River estuary,Australia

The evolution of the entrance channel of the Snowy River estuary in response to river regulation and climate change is predicted. The predictions are made in terms of the physical attractors that define possible long‐term states of the estuary entrance condition. The classification of these attractors shows the dependence of the entrance stability on the catchment inflows and the present entrance depth. The Snowy River estuary in south‐eastern Australia is a barrier estuary with an unstable entrance that tends to closure. The classification from the attractor map shows that the estuary entrance has changed from predominantly stable to a predominantly unstable state attributable to diversion of water from the upper catchment. The introduction of a series of environmental flow regimes, commencing in 2002, has returned 8% rising to 21% of the mean annual natural flow, but this study shows that the releases provide limited improvement in entrance stability. Additionally, the predicted effects of climate change for this region include increased mean sea level (MSL), decreased annual rainfall, and increased incidence of storms. These changes will decrease stability, primarily through the rise in MSL. The rise in sea level will increase the plan area of the tidal basin, increasing the tidal prism, and hence drawing in more marine sand. The application to the Snowy River estuary provides a proof of concept of the attractor classification to support estuary management.     

一种正交多项式混沌全局建模方法

本文研究了一种正交多项式混沌全局建模方法 ,所用正交多项式集以吸引子不变测度为核 .通过对H啨ｎｏｎ映射数据和电离层参数实测数据的分析 ,表明在待建模系统不很复杂时 (其内在机理可用较低阶多项式表达 ) ,这种全局建模方法能得到系统动力学特性 .在低噪声情况下模型还能充分精确地重构系统方程式 .在噪声较大或系统内在机理很复杂时建模结果仍可用于一步预测 ,且具有较好效果     

磨合过程摩擦振动混沌吸引子演变规律

在CFT-I型试验机上进行摩擦副磨合试验,应用混沌理论研究摩擦振动吸引子,探讨磨合过程中摩擦振动混沌吸引子的演变规律。结果表明,摩擦振动吸引子在相空间一定区域内具有特定层次结构且永不封闭轨迹。摩擦振动具有混沌行为的基本特征;随磨损过程的进行,摩擦振动混沌吸引子逐渐收缩并趋于稳定,混沌吸引子变化能反映摩擦副从磨合磨损到稳定磨损状态变化;摩擦振动混沌吸引子体积变化可用于摩擦副的磨合磨损状态预测与识别。