Chaos Solitons & Fractals最新文献_第3页

Deep sparse autoencoders-based community detection and resilience analysis of interdependent infrastructure networks 基于深度稀疏自动编码器的群落检测和相互依存基础设施网络的弹性分析

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-11 DOI: 10.1016/j.chaos.2024.115720

Shuliang Wang, Jin Wang, Shengyang Luan, Bo Song

This paper considers the global information of nodes and constructs a similarity matrix based on s-hop counts. It effectively extracts low-dimensional feature matrices from high-dimensional data to achieve community detection results by utilizing deep learning techniques and deep sparse autoencoders. We successfully detect communities and identify critical inter-community edges. Additionally, we delve into the influence of vulnerable inter-community edges on the resilience of interdependent networks. To illustrate this, a widely employed artificial interdependent power-communication network is adopted as a case study, examining various failure intensities and coupling modes. This approach allows visualization communities, and the impact of vulnerable edges on the interdependent network's resilience is investigated from both structural and functional perspectives. Results have shown that damage to edges bridging different communities can lead to severe network vulnerability. Accordingly, prioritizing the security of these edges will strengthen the network's resilience, which is crucial for preventing further network damage.

本文考虑了节点的全局信息，并基于 s-hop 计数构建了一个相似性矩阵。通过利用深度学习技术和深度稀疏自动编码器，它能有效地从高维数据中提取低维特征矩阵，从而实现社群检测结果。我们成功地检测到了社区，并识别出了社区间的关键边缘。此外，我们还深入研究了脆弱的社群间边缘对相互依存网络恢复能力的影响。为了说明这一点，我们采用了一个广泛使用的人工相互依赖电力通信网络作为案例，研究了各种故障强度和耦合模式。这种方法允许可视化社区，并从结构和功能两个角度研究了脆弱边缘对相互依存网络复原力的影响。结果表明，连接不同群落的边缘受损会导致严重的网络脆弱性。因此，优先保证这些边缘的安全将增强网络的复原力，这对防止网络进一步受损至关重要。

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引用次数: 0

Three-dimensional m-HR neuron model and its application in medical image encryption 三维 m-HR 神经元模型及其在医学图像加密中的应用

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-10 DOI: 10.1016/j.chaos.2024.115701

Qianqian Shi , Shaocheng Qu , Xinlei An , Ziming Wei , Chen Zhang

Theoretical research on neuronal dynamics is crucial for elucidating neural functions of the human brain, and electromagnetic fields significantly influence the electrical activity of neurons. This paper proposes a flux-controlled memristor and analyzes its frequency and amplitude dependent pinched hysteresis loops. Considering the electromagnetic induction effect of the memristor, a novel memristive Hindmarsh–Rose (m-HR) neuron model is constructed, which exhibits the coexistence of asymmetric hidden attractors. The theoretical analyses and simulation results on the Hamilton energy demonstrate that the energy evolution of the m-HR neuron model is predominantly associated with state variables. Subsequently, the intricate discharge patterns of the model are investigated through one-parameter and two-parameter bifurcation analysis, accompanied by complexity assessment. Based on the model, a medical image encryption scheme is devised, capable of simultaneously encrypting multiple images of arbitrary size and type. Additionally, the proposed cross-plane scrambling scheme can effectively minimize pixel correlation. Finally, the security tests indicate that the encryption scheme possesses high security and can effectively withstand diverse attacks.

神经元动力学的理论研究对于阐明人脑的神经功能至关重要，而电磁场会显著影响神经元的电活动。本文提出了一种通量控制忆阻器，并分析了其与频率和振幅相关的捏合磁滞环。考虑到忆阻器的电磁感应效应，本文构建了一种新型忆阻器 Hindmarsh-Rose 神经元（m-HR）模型，该模型表现出非对称隐吸引子共存的特点。对汉密尔顿能量的理论分析和仿真结果表明，m-HR 神经元模型的能量演化主要与状态变量有关。随后，通过单参数和双参数分岔分析以及复杂性评估，研究了该模型错综复杂的放电模式。基于该模型，设计了一种医学图像加密方案，能够同时加密任意大小和类型的多幅图像。此外，所提出的跨平面加扰方案能有效降低像素相关性。最后，安全性测试表明，该加密方案具有很高的安全性，能有效抵御各种攻击。

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引用次数: 0

Auto-resonance process under the interaction of solitons with external force and dissipation 孤子与外力和耗散相互作用下的自共振过程

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-09 DOI: 10.1016/j.chaos.2024.115712

Marcelo V. Flamarion , Efim Pelinovsky

Algebraic soliton interactions with an external force in the presence of Reynolds viscosity is investigated. In the absence of an external force, the soliton amplitude decays over time. However, when an external force is introduced, it acts as a restoring force, and in some cases, the soliton’s amplitude is preserved. A dynamical system that governs the soliton amplitude and its crest position is obtained assuming a weak force and weak viscosity. For an external force with a Gaussian shape, the dynamical system has two equilibrium points, namely, a saddle and a stable spiral. Asymptotic results are compared with direct numerical simulations, and a strong qualitative agreement is observed. The stable spiral predicted by the asymptotic theory is stable in the sense that soliton solutions with a chosen amplitude and crest position near the spiral point are attracted to it, preserving their amplitude and location.

研究了存在雷诺粘度时代数孤子与外力的相互作用。在没有外力的情况下，孤子振幅随时间衰减。然而，当引入外力时，外力会起到恢复力的作用，在某些情况下，孤子的振幅会保持不变。假设外力很弱，粘度也很弱，那么就可以得到一个支配孤子振幅及其波峰位置的动力系统。对于高斯形状的外力，动力学系统有两个平衡点，即鞍形和稳定的螺旋形。将渐近结果与直接数值模拟进行了比较，发现两者在质量上非常一致。渐近理论预测的稳定螺旋是稳定的，即螺旋点附近具有选定振幅和波峰位置的孤子解会被吸引到螺旋点，并保持其振幅和位置。

引用次数: 0

Nonlinear sensitivity and optimization of heat transfer and drag in power law fluid flow over a permeable wedge with variable magnetic field and thermal radiation effects 具有可变磁场和热辐射效应的渗透楔上幂律流体流动中传热和阻力的非线性敏感性与优化

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-09 DOI: 10.1016/j.chaos.2024.115717

Wajiha Waheed , Abuzar Ghaffari , Irfan Mustafa , Rab Nawaz

One of the UN Sustainable Development Goals (SDGs) focuses on preventing energy waste while meeting human energy demands. To contribute to this goal, we optimize the drag force and heat transfer rate in the boundary layer flow of a power-law fluid under the influence of a variable magnetic field and thermal radiation along a nonlinear stretching/shrinking permeable wedge. This optimization is achieved through sensitivity analysis using response surface methodology (RSM). Initially, data is collected using the built-in numerical scheme bvp4c to solve the nonlinear local non-similar problem derived from the Navier-Stokes and the energy equations. The impact of stretching/shrinking wedge along with thermal radiation in both pseudoplastic and dilatant fluids on velocity and temperature profiles, Nusselt number, and skin friction coefficient are discussed graphically. RSM is employed to perform regression analysis and develop expressions for the skin friction and Nusselt number as functions of the coded variables A, B, and C (representing the power law index n, thermal radiation parameter Rd, and velocity ratio parameter ϕ). The optimal impact of these factors is presented in graphs that discuss the sensitivity of skin friction and Nusselt number. From the results, it is revealed that skin friction coefficient is more sensitive to the velocity ratio parameter and Nusselt number is more sensitive to radiation parameter at low and medium levels of power law index and radiation, but it becomes more sensitive to velocity ratio parameter at high level.

联合国可持续发展目标（SDGs）的重点之一是在满足人类能源需求的同时防止能源浪费。为了实现这一目标，我们优化了幂律流体在可变磁场和热辐射影响下沿非线性拉伸/收缩渗透楔的边界层流动中的阻力和传热速率。这种优化是通过使用响应面方法（RSM）进行敏感性分析实现的。最初，使用内置数值方案 bvp4c 收集数据，以解决由纳维-斯托克斯方程和能量方程导出的非线性局部非相似问题。在假塑性流体和膨胀性流体中，拉伸/收缩楔以及热辐射对速度和温度曲线、努塞尔特数和表皮摩擦系数的影响以图表形式进行了讨论。采用 RSM 进行回归分析，并开发出皮肤摩擦系数和努塞尔特数的表达式，作为编码变量 A、B 和 C（代表幂律指数 n、热辐射参数 Rd 和速度比参数 j）的函数。这些因素的最佳影响通过讨论表皮摩擦和努塞尔特数敏感性的图表呈现出来。结果表明，在中低幂律指数和辐射水平下，皮肤摩擦系数对速度比参数更敏感，而努塞尔特数对辐射参数更敏感，但在高水平下，皮肤摩擦系数对速度比参数更敏感。

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引用次数: 0

Wavefunction engineering using Mandelbrot, multicorn, and Koch's snowflake fractal quantum rings to control the persistent current 利用曼德尔布罗特、多角和科赫雪花分形量子环的波函数工程来控制持久电流

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-09 DOI: 10.1016/j.chaos.2024.115706

Davood Haji Taghi Tehrani , M. Solaimani , M.R. Fathollahi

In this work, we have considered the wavefunction, energy levels, and persistent current of two-dimensional quantum rings that created from the less-studied Mandelbrot, multicorn, and Koch's snowflake fractal shapes. The effect of fractality order on the persistent current for different fractal structure, exchanging this fractals as inner and outer border of the rings, composition parameter x in Ga_1−xAl_xAs/GaAs system are studied. For this purpose, the numerical solution of the Schrödinger equation governing the problem has been used. We study the effect of symmetry on the creation and destruction of the persistent current. Besides, we have addressed the degeneracies of the wave function of the structures mentioned above.

在这项工作中，我们研究了二维量子环的波函数、能级和持久电流，这些二维量子环是由研究较少的曼德勃罗分形、多角形和科赫雪花形分形产生的。在 Ga1-xAlxAs/GaAs 体系中，研究了不同分形结构下分形阶数对持久电流的影响、交换这些分形作为环的内外边界以及组成参数 x。为此，我们使用了薛定谔方程的数值解法。我们研究了对称性对持久电流产生和破坏的影响。此外，我们还研究了上述结构波函数的退化性。

引用次数: 0

Stability analysis of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads 横向磁场和热负荷下轴向移动粘弹性梁的稳定性分析

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-08 DOI: 10.1016/j.chaos.2024.115726

Sihan Wu , Xudong Gu , Bingxin Zhao , Zichen Deng

Slender flexible structures in electronic devices and spacecraft usually operate in complex thermal and magnetic environments, in which the stability is greatly affected by the complex environments. In this paper, an analytical method is proposed to study the stability of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads. Firstly, the nonlinear control equation of the axially moving viscoelastic beam is derived by using Hamilton principle, in which the effects of the thermal loads, magnetic field variations and nonlinear deformation of the beam are considered based on the principle of magnetoelasticity. Secondly, Galerkin's method was applied to the derived continuous model to obtain the discrete differential equations of each vibrating mode. Finally, the incremental harmonic balance (IHB) method was employed to determine the unstable regions in the parameter space. The influences of the thermal load, axially moving velocity of the beam, viscosity coefficient, and magnetic field intensity on the regions of stability are investigated. It is found that the thermal loads, axially moving velocity and magnetic field intensity exert a significant influence on the unstable region. The derived results take into account of the combined effects of magnetic field and thermal variation, which is beneficial in understanding the stability of axially moving beams under complex magnetic and thermal environment.

电子设备和航天器中的细长柔性结构通常工作在复杂的热环境和磁场环境中，其稳定性受复杂环境的影响很大。本文提出了一种分析方法来研究轴向运动粘弹性梁在横向磁场和热载荷作用下的稳定性。首先，利用汉密尔顿原理推导出轴向运动粘弹性梁的非线性控制方程，其中根据磁弹性原理考虑了热载荷、磁场变化和梁的非线性变形的影响。其次，对推导出的连续模型应用 Galerkin 方法，得到各振动模式的离散微分方程。最后，采用增量谐波平衡法（IHB）确定参数空间中的不稳定区域。研究了热负荷、梁的轴向移动速度、粘滞系数和磁场强度对稳定区域的影响。结果发现，热负荷、轴向移动速度和磁场强度对不稳定区域有显著影响。得出的结果考虑了磁场和热变化的综合影响，这有利于理解复杂磁场和热环境下轴向移动横梁的稳定性。

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引用次数: 0

An adaptive exploration mechanism for Q-learning in spatial public goods games 空间公共产品博弈中 Q 学习的自适应探索机制

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-07 DOI: 10.1016/j.chaos.2024.115705

Shaofei Shen , Xuejun Zhang , Aobo Xu , Taisen Duan

The Q-learning algorithm has been widely applied to investigate the emergence of cooperation in social dilemmas. Despite

ϵ

-greedy being the most common exploration strategy in Q-learning, mechanisms for adjusting exploration as the game environment changes have not been thoroughly researched. To stay close to reality, this paper proposes an environment-adaptive exploration-based Q-Learning algorithm. We applied the registration concept from image processing to characterize agents’ sensitivity to changes in their surrounding environment to obtain local stimulation. Additionally, we calculated the advantage differences between the agent and the global environment to acquire global stimulation. Simulation results on the public goods game show that the level of cooperation increases and the fraction of exploration consequently decreases when the agents focus more on the local environment. However, the impact of the basic exploration rate on the level of cooperation is not uniform: when the enhancement factor is low, an increase in the exploration rate promotes cooperation, while when the enhancement factor is high, increasing the exploration rate reduces the level of cooperation. The basic exploration rate directly affects the fraction of exploration. Therefore, increasing the basic exploration rate can stably increase the fraction of exploration of the agents. Similarly, the effect of the memory strength parameter

λ

on the level of cooperation is positively correlated, and increasing the value of

λ

increases the level of cooperation across the board. These evolutionary dynamics could enrich the understanding of cooperation in complex systems.

Q-learning 算法已被广泛应用于研究社会困境中合作的出现。尽管ϵ-贪婪是 Q-learning 中最常见的探索策略，但随着游戏环境的变化而调整探索的机制尚未得到深入研究。为了贴近现实，本文提出了一种基于环境自适应探索的 Q-Learning 算法。我们运用图像处理中的注册概念来描述代理对周围环境变化的敏感性，从而获得局部刺激。此外，我们还计算了代理与全局环境之间的优势差异，以获得全局刺激。公共物品博弈的模拟结果表明，当代理更多关注局部环境时，合作水平会提高，探索部分也会随之减少。然而，基本探索率对合作水平的影响并不一致：当增强因子较低时，增加探索率会促进合作，而当增强因子较高时，增加探索率会降低合作水平。基本勘探率直接影响勘探分率。因此，提高基本探索率可以稳定地提高代理的探索率。同样，记忆强度参数 λ 对合作水平的影响也是正相关的，增加 λ 值可以全面提高合作水平。这些进化动力学可以丰富对复杂系统中合作的理解。

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引用次数: 0

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation 爱因斯坦的时空曲率与引力波：阐明标量不变量的梯度流、利玛窦标量的变化和引力波传播

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-06 DOI: 10.1016/j.chaos.2024.115707

Najeh Rekik , Bachir Ouari

In the general theory of relativity initially rationalized by Einstein, the gravity is considered as an occurrence ensuing from the spacetime curvature, which is in turn triggered by the presence of mass. This article provides a detailed analysis of spacetime curvature and gravitational waves, enhancing our understanding of general relativity and astrophysics. Using both analytical and numerical methods, we examined the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation. New findings include the identification of unique curvature patterns around rotating black holes, a detailed comparison of gradient flow behavior in different spacetime geometries, and the discovery of a correlation between scalar invariant fluctuations and gravitational wave amplitudes. These findings validate numerical techniques and reveal how different parameters affect gravitational wave characteristics. While simplified models are used, the present study offers a robust framework for future research. Our work aligns with previous studies but also reveals unique aspects of wave behavior, with implications for quantum gravity and cosmology.

在爱因斯坦最初提出的广义相对论中，引力被认为是由时空曲率引起的，而时空曲率又是由质量的存在引发的。本文详细分析了时空曲率和引力波，加深了我们对广义相对论和天体物理学的理解。利用分析和数值方法，我们研究了标量不变量的梯度流、利玛窦标量的变化和引力波传播。新发现包括确定了旋转黑洞周围的独特曲率模式，详细比较了不同时空几何中的梯度流行为，并发现了标量不变量波动与引力波振幅之间的相关性。这些发现验证了数值技术，并揭示了不同参数如何影响引力波特性。虽然使用的是简化模型，但本研究为未来研究提供了一个稳健的框架。我们的工作与之前的研究相一致，但也揭示了波行为的独特方面，对量子引力和宇宙学产生了影响。

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引用次数: 0

Emergence of relaxation beat-waves in genuinely nonlinear Klein-Gordon chain with bi-harmonic parametric excitation 具有双谐波参数激励的真正非线性克莱因-戈登链中弛豫节拍波的出现

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-05 DOI: 10.1016/j.chaos.2024.115692

Majdi Gzal, Victor Kislovsky, Yuli Starosvetsky

This paper provides analytical investigation of nonstationary regimes in a strongly anharmonic Klein-Gordon chain subjected to the two-component parametric excitation. We explore the mechanisms of formation and provide a comprehensive analytical characterization of the dynamics of two distinct highly nonstationary beat-wave regimes, namely the weakly- and strongly- modulated beat-waves. To this end, we derive the double parametrically driven discrete p-Schrodinger model in the neighborhood of 2:2:1 parametric resonance. The obtained non-autonomous slow-flow model depicts the low-energy complex amplitude modulations of coupled oscillators in the vicinity of 2:2:1 resonance. Through a special coordinate transformation, we exactly reduce the slow-flow system dynamics to a beat-wave slow invariant manifold governed by three collective coordinates. To study the complex nonstationary dynamics of beat-waves, we further reduce the overall system dynamics onto the super-slow invariant manifold (SSIM) by applying an additional multi-scale procedure to the system of collective coordinates. Analysis of the system dynamics on the SSIM reveals the two types of non-stationary beat-wave regimes. The first type is a weakly modulated beat-wave response, exhibiting super-slow amplitude modulation without amplitude relaxation. The second, more intriguing type is a strongly modulated beat-wave response, which exhibits rapid amplitude relaxations characterized by two distinct behaviors: one involving rapid amplitude decay to the trivial state, and the other manifested by the recurrent relaxation oscillations. We derive analytical approximations that describe the mechanisms of formation and the entire dynamics of these highly nonstationary beat-wave states. Remarkably, the analytical model aligns satisfactorily with numerical simulations for both weakly and strongly modulated beat-wave states.

本文对受到双分量参数激励的强非谐克莱因-戈登链中的非稳态进行了分析研究。我们探讨了两种不同的高度非稳态拍波机制（即弱调制拍波和强调制拍波）的形成机制，并对其动力学特性进行了全面的分析。为此，我们推导了 2:2:1 参数共振附近的双参数驱动离散 p 薛定谔模型。得到的非自治慢流模型描述了耦合振荡器在 2:2:1 共振附近的低能复振幅调制。通过特殊的坐标变换，我们将慢流系统动力学精确还原为由三个集合坐标支配的节拍波慢不变流形。为了研究节拍波的复杂非稳态动力学，我们通过对集合坐标系应用额外的多尺度程序，进一步将整个系统动力学还原为超慢不变流形（SSIM）。对 SSIM 上系统动力学的分析揭示了两种非稳态节拍波状态。第一种是弱调制节拍波响应，表现出超慢振幅调制而无振幅松弛。第二种更有趣的类型是强调制节拍波响应，它表现出快速的振幅松弛，有两种不同的行为特征：一种是振幅快速衰减到微不足道的状态，另一种则表现为反复出现的松弛振荡。我们推导出分析近似值，描述了这些高度非稳态节拍波状态的形成机制和整个动力学过程。值得注意的是，分析模型与弱调制和强调制节拍波状态的数值模拟结果都非常吻合。

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引用次数: 0

Impulsive quasi-containment control in stochastic heterogeneous multiplex networks 随机异构多路复用网络中的脉冲准遏制控制

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-05 DOI: 10.1016/j.chaos.2024.115666

Xin Jin , Zhengxin Wang , Xiaojie Chen

In this work, we propose a model for heterogeneous multiplex networks with stochastic perturbations. We consider multiple leaders in the networks and design an impulsive controller for cost saving to investigate the containment control problem in the stochastic heterogeneous multiplex networks. By means of the Lyapunov function method and stochastic impulsive differential equations theory, we obtain sufficient conditions in which the states of all followers converge to the bounded convex hull spanned by the states of multiple leaders. We also obtain the upper bound of the convergence region of the synchronization error system. Furthermore, we study the case with time delay and derive the sufficient conditions for the states of synchronization error to converge to the bounded region. Finally, we give two numerical examples to verify the theoretical results.

在这项工作中，我们提出了一个具有随机扰动的异构多路复用网络模型。我们考虑了网络中的多个领导者，并设计了一个用于节约成本的脉冲控制器，以研究随机异构多路复用网络中的遏制控制问题。通过 Lyapunov 函数方法和随机脉冲微分方程理论，我们得到了所有跟随者的状态收敛到多个领导者状态所跨的有界凸壳的充分条件。我们还得到了同步误差系统收敛区域的上界。此外，我们还研究了有时间延迟的情况，并推导出同步误差状态收敛到有界区域的充分条件。最后，我们给出了两个数值示例来验证理论结果。

引用次数: 0