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.

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.

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.

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.

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.

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。

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.

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.

单自由度含干摩擦碰撞振动系统周期运动转迁及共存特征

在参数平面和状态平面内,研究了一类单自由度含干摩擦和弹性约束碰撞振动系统周期运动的分布、转迁及共存特征。首先,给出了系统各运动状态(滑动、黏着及碰撞)的衔接条件,并利用响应微扰计算方法得到系统的Floquet矩阵。其次,由相轨线与黏着面的关系将系统在参数平面内的运动划分为六种类型,根据Floquet乘子和滑移分岔发生的几何条件判定相邻周期运动在转迁时的稳定性和分岔类型,并基于胞映射和打靶法分析稳定及不稳定周期运动共存及转迁特征。研究发现,在相邻的多态共存区边界线交点处,系统在不同初始状态下存在分岔共存现象。由于间隙和干摩擦广泛存在于实际机械系统中,研究此类系统的动力学特性,对后续系统参数的设计及各种动力学行为的控制具有重要的意义。

具临界指数的非线性阻尼梁方程的全局吸引子

研究具有非线性阻尼梁方程的全局吸引子。当非线性项的增长为临界时,在不假设阻尼参数的最大值的情况下,证明全局吸引子的存在性、正则性和有限维数。

基于改进跟踪微分器的电磁悬浮控制系统研究

在电磁悬浮(EMS)控制系统中,如何实现间隙及间隙微分信号的有效提取是提升系统控制性能的关键问题。针对当前跟踪微分器(TD)存在的综合控制函数形式复杂、参数整定繁琐、输出存在抖振等问题,设计了一种改进的非线性跟踪微分器,旨在提升传感器信号的提取质量。首先通过引入反平方根函数与终端吸引子函数,设计了新型的跟踪微分器。之后应用稳定性理论对改进跟踪微分器的收敛性进行验证,并通过扫频测试进行频域特性分析,明确了该跟踪微分器的参数整定原则。最后进行了闭环控制系统仿真与实物验证,结果表明,ISRU-TD相对于其他3种TD方法在稳态误差方面表现出显著优势。输出位置信号的稳态误差减小了92.58%,相对于ATD减小了18.18%,相对于Fhan-TD减小了42.55%,而与HSTD相比则增加了3.7%。此外,ISRU-TD使输出位置信号的调节时间显著减小,相对于ATD减小了38.68%,相对于Fhan-TD减小了61.99%,相对于HSTD减小了58.06%。表明其具有出色的信号跟踪和噪声抑制能力。

具有共存吸引子混沌系统的自适应同步控制

在一个三维混沌系统的基础上,通过添加一个非线性反馈控制器,得到一个新的四维混沌系统。通过相图、功率谱、庞加莱截面、李雅普诺夫指数、平衡点等证明了系统的混沌特性,并通过分岔图分析了系统在不同参数下的运动状态。研究发现,该系统具有非常复杂的动力学行为和共存吸引子现象。同时,通过设置不同的初始值和不同的偏移增量,分别证明了系统具有共存吸引子,此结论对混沌保密通信等领域有一定的应用价值。通过0-1测试证明了混沌和周期运动的存在,并通过谱熵(spectral entropy,SE)算法和C0算法讨论了系统的复杂度。最后,设计了自适应同步控制器,仿真结果证明新系统可以在参数不确定的情况下实现同步控制,表明控制器是有效的。

随机反应扩散方程的随机吸引子的高阶稳定性

本文研究带加性白噪声的随机反应扩散方程的随机吸引子关于噪声强度的稳定性。首先,在非线性函数满足更一般条件下,在初始空间L^(2)(R^(N))中获得随机微分方程的解收敛到确定方程的解,从而得到随机吸引子的上半连续性;然后,利用非线性分解和差分估计,证明L^(p)(R^(N))(p>2)空间中解的收敛性和随机吸引子的上半连续性,其中p是非线性函数的增长指数。

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Research on discrete memristor-based neural networks has received much attention.However,current research mainly focuses on memristor–based discrete homogeneous neuron networks,while memristor-coupled discrete heterogeneous neuron networks are rarely reported.In this study,a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V–I diagram.Based on two-dimensional(2D)discrete Izhikevich neuron and 2D discrete Chialvo neuron,a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons.Considering the coupling strength as the control parameter,chaotic firing,periodic firing,and hyperchaotic firing patterns are revealed.In particular,multiple coexisting firing patterns are observed,which are induced by different initial values of the memristor.Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength.Furthermore,the effect of Gaussian white noise on synchronization behaviors is also explored.We demonstrate that the presence of noise not only leads to the transition of firing patterns,but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Synaptic crosstalk is a prevalent phenomenon among neuronal synapses,playing a crucial role in the transmission of neural signals.Therefore,considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks are highly necessary.In this paper,we propose a heterogeneous discrete neural network(HDNN)consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron.These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered.The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents.It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths.Furthermore,the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated,revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.