Bipolar-growth multi-wing attractors and diverse coexisting attractors in a new memristive chaotic system

This article proposes a non-ideal flux-controlled memristor with a bisymmetric sawtooth piecewise function, and a new multi-wing memristive chaotic system(MMCS) based on the memristor is generated. Compared with other existing MMCSs, the most eye-catching point of the proposed MMCS is that the amplitude of the wing will enlarge towards the poles as the number of wings increases. Diverse coexisting attractors are numerically found in the MMCS, including chaos,quasi-period, and stable point. The circuits of the proposed memristor and MMCS are designed and the obtained results demonstrate their validity and reliability.

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

Evidence of the Great Attractor and Great Repeller from Artificial Neural Network Imputation of Sloan Digital Sky Survey

The Sloane Digital Sky Survey (SDSS) has been in the process of creating a 3D digital map of the Universe, since 2000AD. However, it has not been able to map that portion of the sky which is occluded by the dust gas and stars of our own Milkyway Galaxy. This research builds on work from a previous paper that sought to impute this missing galactic information using Inpainting, polar transforms and Linear Regression ANNs. In that paper, the author only attempted to impute the data in the Northern hemisphere using the ANN model, which subsequently confirmed the existence of the Great Attractor and the homogeneity of the Universe. In this paper, the author has imputed the Southern Hemisphere and discovered a region that is mostly devoid of stars. Since this area appears to be the counterpart to the Great Attractor, the author refers to it as the Great Repeller and postulates that it is an area of physical repulsion, inline with the work of GerdPommerenke and others. Finally, the paper investigates large scale structures in the imputed galaxies.

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.

A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control

This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.

Complexity analyses of multi-wing chaotic systems

The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.

THEORETICAL RESULTS ON THE EXISTENCE,REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS:APPLICATIONS TO 3D PRIMITIVE EQUATIONS

Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.

Dynamical analysis and anti-synchronization of a new 6D model with self-excited attractors

A novel 6D dissipative model with an unstable equilibrium point is introduced herein.Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical points,stability,Lyapunov exponents,time phase portraits,and circuit implementation.Also,anti-synchronization phenomena were implemented on the new system.Firstly,the error dynamics is found.Then,four different controllers are adopted to stabilize this error relying on the nonlinear control technique with two main ways:linearization and Lyapunov stability theory.In comparison with previous works,the present controllers realize anti-synchronization based on another method/linearization method.Finally,a comparison between the two ways was made.The simulation results show the effectiveness and accuracy of the first analytical strategy.

Corrigendum to “The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation andcoexisting attractors”

Recently, we received a letter from Prof. G. L. Oppo, which indicated that he had doubts about the transformation of the system in the article Chin. Phys. B 31 060503 (2022) and gave other considerations. After inspection, we found that there was a clerical error in the article. Based on this, we have made corrections and supplements to the original article.

STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS

We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.

How to Make Systems of Nonlinear Autonomous ODEs with Attractor-Behavior, by First Making the General Solutions: Part Two

This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine, and cosine. We are building up the general solutions bit for bit according to constant terms that contain the formula of the desired limit cycle, and differentiating them. In Part One, we used only formulas for closed curves where all parts of the formula were of the same degree. In order to use many other formulas for closed curves, the method in this paper is to introduce an additional variable, and we will get an additional ODE. We will choose the part of the formula with the highest degree and multiply the other parts with an extra variable, so that all parts of the formula have the same degree, creating a constant term containing this new formula. We will place it under the fraction line in the solutions, building up the rest of the solutions according to this constant term and differentiating. Keeping this extra variable constant, we will achieve almost the desired result. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions and some surfaces having attractor behavior, where not all parts of the formulas are the same degree. The pictures show the result.

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The parameter switching algorithm is used to numerically study the dynamic behaviors of the system.Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors.A self-excited attractor with the change of its parameters is also recognized.In addition,numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra,Lyapunov dimensions,bifurcation diagrams,phase space orbits,and basins of attraction.Consequently,the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable.These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems,and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.

A Family of Global Attractors for the Generalized Kirchhoff-Beam Equations

In this paper, we discuss the existence and uniqueness of global solutions, the existence of the family of global attractors and its dimension estimation for generalized Beam-Kirchhoff equation under initial conditions and boundary conditions, using the previous research results for reference. Firstly, the existence of bounded absorption set is proved by using a prior estimation, then the existence and uniqueness of the global solution of the problem is proved by using the classical Galerkin’s method. Finally, Housdorff dimension and fractal dimension of the family of global attractors are estimated by linear variational method and generalized Sobolev-Lieb-Thirring inequality.

动作时序优化振动信号混沌吸引子特征的断路器操动状态辨识方法

高压断路器分合闸操作过程包括掣子脱扣、弹簧释能、动静触头碰撞等动作,机械振动信号作为能量传递的表现,蕴含着丰富的运行状态信息。该文基于断路器关键动作节点的时序,提出一种动作时序优化振动信号混沌吸引子特征的断路器操动状态辨识方法。首先,由高速相机捕捉断路器操动过程主轴拐臂运动图像,利用目标跟踪算法获取动触头关键运动节点时序指标;然后,依据时序指标划分操动过程,通过对不同阶段的振动信号相空间重构,提取相空间吸引子几何和属性特征;最后,利用智能分类算法进行故障辨识,实验结果验证该方法在大幅节省时间开销的同时,有效提高了分类辨识的准确率达96.9%。该文方法在断路器状态监测和带电测试中具有广阔应用前景。

带有分布时滞吊桥方程一致吸引子

考虑当依赖于时间的外力项平移有界而非平移紧时,内部反馈阻尼项含有分布时滞的以矩形板为模型的吊桥方程解的长时间动力学行为.首先,应用单调极大算子理论讨论了该方程解的适定性,进一步应用压缩函数方法证明过程族是一致渐近紧的,从而得到一致吸引子的存在性.

齿轮传动系统共存吸引子的稳定性与分岔

以3自由度齿轮传动系统为研究对象,应用数值仿真方法得到系统的多初值分岔图,结合最大Lyapunov指数(Top Lyapunov Exponent,TLE)分析阻尼系数对系统动力学特性的影响。将数值仿真、延拓打靶法和Floquet特征乘子相结合,延拓追踪共存吸引子的稳定性与分岔。应用胞映射法计算共存吸引子的吸引域,结合分岔图、相图和Poincaré映射图揭示共存吸引子的吸引域随系统参数变化的侵蚀演变过程。结果表明:系统存在周期倍化分岔点和鞍结分岔点之间的距离非常近的现象,鞍结分岔使系统终态在两个不同的周期运动之间跳跃,使周期倍化分岔表现出亚临界特性;共存的周期吸引子主要由鞍结分岔引起;若鞍结分岔发生在概周期运动区间,则会出现周期吸引子与概周期吸引子共存。

电磁感应下分数阶神经网络动力学行为分析及应用

忆阻器可以用来模拟生物神经突触和描述电磁感应效应.为了探索电磁感应作用下异构神经网络的动力学行为,本文首先使用双局部有源忆阻器耦合一个Hindmarsh-Rose (HR)和两个FitzHugh-Nagumo (FN)神经元,构成忆阻电磁感应下分数阶异构神经网络.然后利用相图、分岔图、李雅普诺夫指数谱和吸引盆等动力学分析方法,对该网络进行数值研究.结果表明该神经网络表现出丰富的动力学行为,包括共存行为、反单调现象、瞬态混沌和放电行为等,为研究人脑放电行为提供支持,随后进一步利用时间反馈控制方法实现了双稳态的控制.最后,在嵌入式硬件平台上实现了该神经网络,验证了仿真结果的有效性.

一种新型复合指数型局部有源忆阻器耦合的Hopfield神经网络

由忆阻耦合的神经网络模型,因其能更真实地反映生物神经系统的复杂动力学特性而被广泛研究.目前用于耦合神经网络的忆阻器数学模型主要集中在一次函数、绝对值函数、双曲正切函数等,为进一步丰富忆阻耦合神经网络模型,且考虑到一些掺杂半导体中粒子的运动规律,设计了一种新的复合指数型局部有源忆阻器,并将其作为耦合突触用于Hopfield神经网络,利用基本的动力学分析方法,研究了系统在不同参数下的动力学行为,以及在不同初始值下多种分岔模式共存的现象.实验结果表明,忆阻突触内部参数对系统具有调控作用,且该系统拥有丰富的动力学行为,包括对称吸引子共存、非对称吸引子共存、大范围的混沌状态和簇发振荡等.最后,用STM32单片机对系统进行了硬件实现.

含预紧弹簧碰撞系统的两参数动力学

考虑含预紧弹簧机械碰撞系统,构建由光滑流映射和不连续映射复合的Poincaré映射,给出Floquet乘子计算的数值方法。数值仿真系统在两参数平面的周期吸引子模式及其参数域,应用延拓打靶法和胞映射法研究周期1吸引子的分岔特征以及不连续擦边分岔、擦边和周期倍化诱导的分岔、亚临界周期倍化分岔和激变等不连续分岔行为,揭示迟滞域和亚谐包含域的形成机理。不连续擦边分岔在相邻1-m与1-(m+1)吸引子的转迁过程中产生迟滞域和亚谐包含域。然而,当预压量等于0时,擦边诱导的鞍结和周期倍化分岔分别产生迟滞域和亚谐包含域。研究结果能够为工程实际含预紧弹簧机械碰撞系统的参数设计与优化提供参考。

无界域上具有记忆的非自治Plate方程随机吸引子的存在性

研究无界域上一类具有衰退记忆和加性噪声的非自治Plate方程解的长时间行为.利用一致估计验证了解的拉回渐近紧性,获得了其随机吸引子的存在性.