Chaos Solitons & Fractals最新文献

英文中文

Dynamics analysis and adaptive neural network command filtering excitation control of stochastic power system 随机电力系统的动态分析和自适应神经网络指令滤波励磁控制

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-01 DOI: 10.1016/j.chaos.2024.115690

New energy sources, such as wind and photovoltaic systems, demonstrate inherent randomness in their power outputs. Additionally, flexible loads, such as electric vehicles at the consumption end further contribute to this variability. These factors result in significant continuous stochastic disturbances on the power system that pose significant threats to the safe and stable operation of the system. Considering continuous stochastic power perturbations, we establish a stochastic differential model of the power system based on Ito stochastic theory. This model analyzes changes in dynamic behavior and oscillation patterns, indicating that stochastic perturbations expand oscillations and reduce the stability boundary. To enhance the system’s security and stability, we propose an adaptive neural network command filter (ANNCF) excitation control method to address stochastic oscillations caused by stochastic power disturbances. Experimental validation using the Real-Time Laboratory (RT-LAB) semi-physical real-time simulation platform shows that the proposed ANNCF excitation method effectively responds to stochastic perturbations, suppresses the stochastic oscillation phenomenon, and significantly improves resistance to stochastic disturbances. Furthermore, this method maintains a superior control effect during sudden power changes and three-phase short circuits, improving the transient stability of the power system.

风能和光伏发电系统等新能源的电力输出具有固有的随机性。此外，灵活负载（如消费端的电动汽车）也进一步加剧了这种可变性。这些因素给电力系统带来了巨大的连续随机干扰，对系统的安全稳定运行构成了严重威胁。考虑到连续随机电力扰动，我们基于伊藤随机理论建立了电力系统的随机微分模型。该模型分析了动态行为和振荡模式的变化，表明随机扰动会扩大振荡并降低稳定性边界。为了提高系统的安全性和稳定性，我们提出了一种自适应神经网络指令滤波器（ANCF）励磁控制方法，以解决随机电力扰动引起的随机振荡问题。利用实时实验室（RT-LAB）半物理实时仿真平台进行的实验验证表明，所提出的 ANNCF 励磁方法能有效响应随机扰动，抑制随机振荡现象，并显著提高抗随机扰动能力。此外，该方法还能在功率突变和三相短路时保持出色的控制效果，提高电力系统的暂态稳定性。

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引用次数: 0

LMI synchronization conditions for variable fractional-order one-sided Lipschitz chaotic systems with gain fluctuations 具有增益波动的可变分数阶单边 Lipschitz 混沌系统的 LMI 同步条件

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-01 DOI: 10.1016/j.chaos.2024.115695

This article addresses the synchronization of general variable fractional-order one-sided Lipschitz chaotic systems with norm-bounded time-varying parametric uncertainty. A non-fragile state feedback control scheme is designed to cope with uncertainties in the controller gain fluctuations, and a sufficient condition for master/slave synchronization and determination of the controller gain is derived and expressed as a linear matrix inequality. The new control approach is applicable to fractional-order Lipschitz chaotic systems as well as to integer-order systems. Additionally, compared with other existing schemes, the method is easier and less costly to implement in real-world applications. Three numerical examples are given to show the performance of the non-fragile control approach for synchronizing practical chaotic systems.

本文探讨了具有规范约束时变参数不确定性的一般可变分数阶单边 Lipschitz 混沌系统的同步问题。本文设计了一种非脆弱状态反馈控制方案来应对控制器增益波动的不确定性，并推导出了主/从同步和确定控制器增益的充分条件，用线性矩阵不等式表示。新的控制方法既适用于分数阶 Lipschitz 混沌系统，也适用于整数阶系统。此外，与其他现有方案相比，该方法在实际应用中更容易实现，成本更低。本文给出了三个数值示例，展示了非脆弱控制方法在同步实际混沌系统方面的性能。

引用次数: 0

Cyclic symmetric dynamics in chaotic maps 混沌图中的循环对称动力学

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-31 DOI: 10.1016/j.chaos.2024.115684

In a recent paper (Liu et al., 2024), we reported on the microscopic mechanism underlying multistability in discrete dynamical systems, suggesting the potential for higher, even arbitrary-dimensional multistability in our conclusions. Before we can validate it, a fundamental question arises: what method can preserve the global dynamics of systems while allowing for an increase in dimensionality? This paper identifies the cyclic symmetric structure as a crucial solution and establishes two two-dimensional maps model based on it. The presence of multistability in any direction is affirmed, with this phenomenon representing either homogeneous or heterogeneous infinite expansion of the medium in multidimensional space. Furthermore, we uncover a range of dynamical characteristics, including grid-like phase trajectories, scale-free attractor clusters, fractal basin structures, symmetric attractors, and chaotic diffusion, all rooted in the system’s symmetric dynamical nature. This research not only enhances the comprehension of high-dimensional symmetric dynamics, but also offers a novel perspective for elucidating related models and phenomena.

在最近的一篇论文（Liu et al., 2024）中，我们报告了离散动力系统多稳定性的微观机制，并在结论中提出了更高、甚至任意维度多稳定性的可能性。在我们验证它之前，一个基本问题出现了：什么方法既能保持系统的全局动力学，又能允许维度的增加？本文认为循环对称结构是一个重要的解决方案，并在此基础上建立了两个二维映射模型。本文肯定了任何方向上的多稳定性的存在，这种现象代表了介质在多维空间中的同质或异质无限扩展。此外，我们还发现了一系列动力学特征，包括网格状相轨迹、无标度吸引子簇、分形盆地结构、对称吸引子和混沌扩散，所有这些都植根于系统的对称动力学性质。这项研究不仅加深了对高维对称动力学的理解，还为阐明相关模型和现象提供了新的视角。

引用次数: 0

Azimuthally dependent spontaneous emission from a coherently microwave-field driven four-level atom-light coupling scheme 相干微波场驱动四级原子-光耦合方案的方位自发辐射

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115672

We present a novel technique that makes use of vortex light beams for generating spatially structured spontaneously emission in a atomic four-level configuration. This atomic configuration consists of two closely spaced excited levels linked to a microwave field and two optical vortex fields connecting them to the ground state. After that, the excited states eventually decays to a fourth metastable level. We find that spatially dependent spontaneous emission spectra may be obtained by efficiently transferring the orbital angular momentum (OAM) of the vortex-pumping light beams to the spontaneously emitted photons. This enables the targeted quenching of spontaneous emission in specific azimuthal regions, while simultaneously enhancing it in others. By effectively controlling the OAM of optical vortices and taking into account the correlations of the atomic gas and their collective decay to a metastable state via superradiance, it might be feasible to experimentally modify the probabilistic emission process with deterministic radiation. The approach we propose might be helpful in controlling the quantum level emission characteristics via the nonlinear interaction of the atom–vortex-beam light.

我们介绍了一种利用涡旋光束在原子四级构型中产生空间结构自发辐射的新技术。这种原子构型包括与微波场相连的两个紧密间隔的激发态，以及将它们与基态相连的两个光学涡旋场。在此之后，激发态最终衰减到第四个陨变水平。我们发现，通过有效地将涡旋泵浦光束的轨道角动量（OAM）转移到自发辐射光子上，可以获得空间相关的自发辐射光谱。这样就能有针对性地淬灭特定方位角区域的自发辐射，同时增强其他区域的自发辐射。通过有效控制光学漩涡的 OAM，并考虑到原子气体的相关性及其通过超辐照度集体衰减到陨变态的情况，用确定性辐射在实验中改变概率发射过程也许是可行的。我们提出的方法可能有助于通过原子-涡旋-光束的非线性相互作用来控制量子级发射特性。

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引用次数: 0

Percolation behavior of partially interdependent networks with capacity and loads 具有容量和负载的部分相互依存网络的渗透行为

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115674

Capacity-loaded networks with interdependent topologies accurately mirror various infrastructure networks. In this work, a partially interdependent network with capacity and loads model is proposed to portray the network structure in real systems. The theoretical framework based on percolation theory for predicting percolation thresholds in partially interdependent networks with capacity and loads is established using generating functions and self-consistent equations. The percolation transition of network is analyzed by initially removing

1 - p

fraction nodes and exploring the size of the giant component of the network after cascade failure. Random and scale-free networks are used for numerical and simulation experiments. We find that increasing the capacity parameter enhances the robustness of interdependent networks and alters the percolation characteristics within the network. The phase transition types in random networks exhibit notable variations across different average degrees, while those in scale-free networks are influenced by power-law exponents. Finally, the validity and accuracy of the proposed model is confirmed by a double-layer empirical network consisting of the World Cities Network and the U.S. Electricity Network.

具有相互依存拓扑结构的容量负载网络能准确反映各种基础设施网络。本文提出了一个具有容量和负载的部分相互依赖网络模型，以描绘真实系统中的网络结构。利用生成函数和自洽方程，建立了基于渗流理论的理论框架，用于预测具有容量和负载的部分相互依赖网络的渗流阈值。通过初始移除 1-p 部分节点和探索级联失效后网络巨大分量的大小，分析了网络的渗滤转变。随机网络和无标度网络被用于数值和模拟实验。我们发现，增加容量参数会增强相互依存网络的鲁棒性，并改变网络内部的渗流特性。随机网络中的相变类型在不同的平均度上表现出明显的差异，而无标度网络中的相变类型则受到幂律指数的影响。最后，由世界城市网络和美国电力网络组成的双层实证网络证实了所提模型的有效性和准确性。

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引用次数: 0

Spiral wave chimeras in nonlocally coupled excitable FitzHugh–Nagumo neurons 非局部耦合可兴奋 FitzHugh-Nagumo 神经元中的螺旋波嵌合体

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115681

Chimera states in excitable systems have received extensive attention in recent years. However, the spiral wave chimera in a two-dimensional excitable system has not been observed yet. In this study, we investigate spiral wave chimeras in two-dimensional nonlocally coupled excitable FitzHugh–Nagumo neurons. Depending on the relative coupling radius and the coupling phase, we find spiral wave chimeras numerically. We also find a novel spiral wave pattern, the spiral wave amplitude death chimera, characterized by a non-excited core. By exploring the phase diagram of different spiral wave chimera dynamics, we find the transition between spiral wave chimeras with an incoherent core and spiral wave amplitude death chimeras with a non-excited core when the coupling phase crosses

π / 2

. We also find that large

a

(the parameter in the FitzHugh–Nagumo neuron) favors the spiral wave amplitude death chimera.

近年来，可激发系统中的嵌合态受到广泛关注。然而，二维可兴奋系统中的螺旋波嵌合态尚未被观测到。在本研究中，我们研究了二维非局部耦合可激 FitzHugh-Nagumo 神经元中的螺旋波嵌合体。根据相对耦合半径和耦合相位，我们在数值上发现了螺旋波嵌合体。我们还发现了一种新的螺旋波模式--螺旋波振幅死亡嵌合体，其特点是有一个非兴奋核心。通过探索不同螺旋波嵌合体动力学的相图，我们发现当耦合相位跨越 π/2 时，具有非相干核心的螺旋波嵌合体与具有非激发核心的螺旋波振幅死亡嵌合体之间发生了过渡。我们还发现，大 a（FitzHugh-Nagumo 神经元中的参数）有利于螺旋波振幅死亡嵌合体。

引用次数: 0

Hybrid control design for nonlinear chaotic semi-Markov jump systems via fault alarm approach 通过故障报警方法进行非线性混沌半马尔可夫跃迁系统的混合控制设计

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115663

This paper investigates the stabilisation problem for a class of T-S fuzzy chaotic semi-Markov jump systems against parametric uncertainties, actuator faults and external disturbances. The main objective of this study is to develop a fault alarm-based non-fragile mode-dependent hybrid controller mechanism to withstand the actuator faults in the concerned system, wherein the hybrid control design blends both robust and fault-tolerant control schemes. Therein, the fault-alarm system is configured based on the alarm threshold, which aids in the execution of the hybrid controller. Specifically, it allows the controller to be timely alerted, making it switch from a robust to a fault-tolerant controller, that is, robust control oversees when the system functions without fault and fault-tolerant control takes over when the system encounters a fault. From there on, through the consideration of relevant Lyapunov function, a novel set of mode-dependent sufficient criteria that have a linear matrix inequality structure is acquired, which confirms the

(X, Y, ℨ)

ζ

-dissipativity of the system under study. Following that, the precise design of the robust and fault-tolerant controller is procured by solving the developed sufficient conditions. In the end, the simulation results of Chua’s circuit system are offered to confirm the significance of the theoretical insights acknowledged.

本文研究了一类 T-S 模糊混沌半马尔可夫跃迁系统在参数不确定性、执行器故障和外部干扰下的稳定问题。本研究的主要目的是开发一种基于故障报警的非脆弱模式依赖混合控制器机制，以抵御相关系统中的执行器故障，其中混合控制设计融合了鲁棒性和容错控制方案。其中，故障报警系统根据报警阈值进行配置，有助于混合控制器的执行。具体来说，它允许控制器及时报警，使其从稳健型控制器切换到容错型控制器，也就是说，当系统无故障运行时，稳健型控制负责监督，而当系统遇到故障时，容错型控制负责接管。从那时起，通过考虑相关的 Lyapunov 函数，获得了一组具有线性矩阵不等式结构的与模式相关的新的充分准则，从而确认了所研究系统的（X,Y,ℨ）-ζ-容错性。随后，通过求解所建立的充分条件，精确设计出鲁棒性和容错性控制器。最后，本文提供了 Chua 电路系统的仿真结果，以证实理论见解的重要性。

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引用次数: 0

Link prediction in multiplex social networks: An information transmission approach 多路社交网络中的链接预测：信息传输方法

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115683

In recent years, link prediction in multiplex networks has attracted increasing interest of researchers. Multiplex social networks that model different types of social relationships between the same set of entities in separate layers are a special case of multiplex networks. However, most existing methods usually ignore that new links can also be formed through information transmission. Therefore, we propose a novel link prediction method that applies information transmission approach to multiplex social networks in this paper. To begin with, we define a new index and three new ways of information transmission in a multiplex network. In this regard, the similarities of potential links in the target layer are computed based on the total amount of information they transmit each other via fusing information from all layers. At last, the interlayer relevance method is used to weight all layers. To evaluate the prediction performance of the proposed method, extensive experiments are implemented on eight real-world multiplex networks, and the experimental results demonstrate that the proposed method significantly outperforms several competing state-of-the-art methods in most cases.

近年来，多重网络中的链接预测引起了研究人员越来越多的兴趣。多重社会网络是多重网络的一种特例，它将同一组实体之间不同类型的社会关系分层建模。然而，大多数现有方法通常忽略了新链接也可以通过信息传输形成。因此，我们在本文中提出了一种新颖的链接预测方法，将信息传递方法应用于多重社会网络。首先，我们定义了一个新指标和复用网络中三种新的信息传输方式。在这方面，目标层中潜在链接的相似性是根据它们通过融合各层信息相互传输的信息总量来计算的。最后，使用层间相关性方法对所有层进行加权。为了评估所提方法的预测性能，我们在八个真实世界的多路复用网络上进行了大量实验，实验结果表明，在大多数情况下，所提方法的性能明显优于几种最先进的竞争方法。

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引用次数: 0

Synthesis of a hybrid control algorithm for chaotifying mechanical systems 混沌化机械系统混合控制算法的合成

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115670

This paper presents a novel hybrid control algorithm for inducing chaos in a limit cycle oscillator by chaotically varying suitable parameters within the chosen bounds. A discrete chaotic map governs the parameter variation at the predetermined Poincaré section. A cubic polynomial mapping is used to obtain the continuous variation between two consecutive crossings at the Poincaré section. A resonant controller with acceleration feedback is designed to implement the proposed control algorithm in a mechanical system with a single degree of freedom. This controller generates a limit cycle at the desired frequency and amplitude. The next step involves using a modified Pomeau-Manneville (PM) map to achieve the chaotification of the limit cycle, which yields a flat Fast Fourier Transform (FFT) of the response within a given bandwidth. The proposed control strategy not only chaotifies the system but also regulates desired response characteristics, such as amplitude, frequency band, chaoticity and power spectral distributions. This is believed to be the first attempt to control the desired characteristics of chaotic response in the case of continuous-time systems. Experiments with an electromagnetic actuator validate the simulation results.

本文提出了一种新颖的混合控制算法，通过在所选范围内混沌改变合适的参数，在极限周期振荡器中诱导混沌。离散混沌映射控制着预定波恩卡莱截面处的参数变化。立方多项式映射用于获得波恩卡莱截面上两个连续交叉点之间的连续变化。为了在单自由度机械系统中实施所提出的控制算法，我们设计了一个带有加速度反馈的谐振控制器。该控制器能以所需的频率和振幅产生一个极限周期。下一步是使用修改后的波莫-曼内维勒（PM）图实现极限周期的混沌化，从而在给定带宽内获得响应的平滑快速傅立叶变换（FFT）。所提出的控制策略不仅能使系统混沌化，还能调节所需的响应特性，如振幅、频带、混沌度和功率谱分布。这是首次尝试在连续时间系统中控制混沌响应的理想特性。电磁致动器的实验验证了模拟结果。

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引用次数: 0

Penetrative convection in Navier–Stokes-Voigt fluid induced by internal heat source 内热源诱导 Navier-Stokes-Voigt 流体中的穿透对流

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-10-30 DOI: 10.1016/j.chaos.2024.115689

This study investigates the phenomenon of penetrative convection in a viscoelastic fluid described by the Navier-Stokes-Kelvin-Voigt (NSKV) model, incorporating internal heat sources and realistic rigid boundary conditions. We examine four distinct space-dependent heat source distributions: constant, linearly increasing, decreasing, and non-uniform across the fluid layer. The Kelvin-Voigt fluid layer is simultaneously heated and salted from the bottom. We employ both linear instability analysis using normal mode technique and nonlinear stability analysis through energy method. The resulting differential eigenvalue systems are treated using the Chebyshev-Spectral-QZ method. Our investigation focuses on the effects of the internal heating parameter, Kelvin-Voigt number, and solute Rayleigh number on the threshold values for convection onset. Our results reveal that internal heat sources destabilize the fluid system, while the salt Rayleigh number contributes to system stabilization. Nonlinear analysis reveals that the total energy of perturbations to the steady-state conduction solutions decays exponentially, and the decay rate is stronger for the Kelvin-Voigt fluid than for Newtonian fluid. Furthermore, the Kelvin-Voigt number acts as a stabilizing factor for the onset of convection, exerting a stabilizing effect on the system. Importantly, the thresholds obtained from linear and nonlinear theories differ in both the presence and absence of internal heat sources, suggesting the existence of a subcritical instability region (SIR). This comprehensive analysis provides new insights into the complex dynamics of penetrative convection in viscoelastic fluids with internal heating.

本研究探讨了由纳维-斯托克斯-开尔文-伏依格特（NSKV）模型描述的粘弹性流体中的穿透对流现象，其中包含内部热源和现实的刚性边界条件。我们研究了四种不同的随空间变化的热源分布：恒定、线性增加、递减和整个流体层的非均匀分布。开尔文-伏依格特流体层同时从底部加热和加盐。我们采用法模技术进行线性不稳定性分析，并通过能量法进行非线性稳定性分析。由此产生的微分特征值系统采用切比雪夫-谱-QZ 方法进行处理。我们的研究重点是内部加热参数、开尔文-伏依格特数和溶质雷利数对对流开始阈值的影响。我们的研究结果表明，内部热源会破坏流体系统的稳定性，而盐的雷利数则有助于系统的稳定。非线性分析表明，对稳态传导解的扰动总能量呈指数衰减，开尔文-伏依格特流体的衰减率比牛顿流体更强。此外，开尔文-伏依格特数是对流开始时的一个稳定因子，对系统起着稳定作用。重要的是，在存在和不存在内部热源的情况下，线性理论和非线性理论得到的阈值都不同，这表明存在亚临界不稳定区域（SIR）。这一综合分析为我们提供了关于具有内部加热的粘弹性流体中穿透对流复杂动力学的新见解。

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