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Modeling cross-modal interactions via a nonlinear information-density-aware network for MAFLD risk assessment 基于非线性信息密度感知网络的MAFLD风险评估跨模态相互作用建模
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-31 DOI: 10.1016/j.chaos.2026.117978
Xiaohua Hu , Xiang Zhu , Jia Shi , Zhaoxian Yan , Shuangshuang Qian , Hanlin Qi , Juan Du , He Yan , Changquan Ling
Modern multimodal learning often requires handling heterogeneous data types whose structures and information densities differ substantially. To address this challenge in the context of metabolic dysfunction-associated fatty liver disease (MAFLD) prediction, we propose an information-density-aware multimodal framework (NID-Net). Instead of relying on simple concatenation or shallow fusion, the model processes each modality using methods that align with its structural characteristics. Structured indicators with high information density are first processed by an XGBoost module optimized via Lagrange remainder correction, which enhances the nonlinearity of the loss landscape and improves robustness to data sparsity and imbalance. Meanwhile, tongue images with relatively low information density are encoded using a region-enhanced Swin Transformer, where adaptive regional biases guide the model toward informative local representations. The resulting modality-specific embeddings are fused within a Mixture-of-Experts (MoE) architecture, enabling selective specialization and nonlinear decision boundaries across modalities. Extensive experiments on real-world medical datasets demonstrate that NID-Net not only surpasses existing multimodal fusion approaches in predictive performance but also provides interpretable insights into cross-modal feature interactions. This work highlights the fundamental role of nonlinear design in achieving efficient, balanced, and explainable multimodal prediction systems.
现代多模态学习通常需要处理结构和信息密度差异很大的异构数据类型。为了在代谢功能障碍相关脂肪肝(MAFLD)预测的背景下解决这一挑战,我们提出了一个信息密度感知的多模式框架(NID-Net)。该模型不依赖于简单的连接或浅融合,而是使用与其结构特征相一致的方法处理每种模态。高信息密度的结构化指标首先通过拉格朗日余数校正优化的XGBoost模块进行处理,增强了损失域的非线性,提高了对数据稀疏性和不平衡的鲁棒性。同时,使用区域增强的Swin Transformer对信息密度相对较低的舌头图像进行编码,其中自适应区域偏差将模型引导到信息丰富的局部表示。生成的特定于模态的嵌入被融合到专家混合(MoE)体系结构中,从而实现了跨模态的选择性专门化和非线性决策边界。在真实医学数据集上的大量实验表明,NID-Net不仅在预测性能上超越了现有的多模态融合方法,而且还提供了对跨模态特征交互的可解释性见解。这项工作强调了非线性设计在实现高效、平衡和可解释的多模态预测系统中的基本作用。
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引用次数: 0
Observation of partial replica symmetry breaking in polarization space for modulation instability competed by self-phase modulation 偏振空间中自相位调制不稳定性的部分复制对称性破缺观察
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-31 DOI: 10.1016/j.chaos.2026.118005
Yu Long, Lei Gao, Ai Liu, Shiyun Dai, Yujia Li, Ligang Huang, Tao Zhu
Replica symmetry breaking provides a profound framework for understanding complex systems. However, a direct experimental confirmation of such complex statistical behavior within the polarization space of a fundamental nonlinear process like modulation instability has remained elusive. Here, exploiting advances in ultrafast optical polarization measurement, we report the first experimental observation of partial replica symmetry breaking in the polarization space, where polarization serves as a direct analogue of spin. By performing wavelength-resolved polarization measurements of modulation instability sidebands, we identify the replica symmetry breaking for specific wavelengths by calculating the overlapping parameter of fluctuations between any two arbitrary points in polarization space, while other wavelengths maintain replica symmetric behavior. The partial replica symmetry breaking in polarization space is attributed to the competition of modulation instability and self-phase modulation. Our results establish polarization as a natural platform for probing complex energy landscapes in disordered photonic systems.
复制对称破缺为理解复杂系统提供了一个深刻的框架。然而,在调制不稳定性等基本非线性过程的极化空间中,这种复杂的统计行为的直接实验证实仍然难以捉摸。在这里,利用超快光学偏振测量的进展,我们报告了偏振空间中部分复制对称破缺的首次实验观察,其中偏振作为自旋的直接模拟。通过对调制不稳定边带进行波长分辨偏振测量,我们通过计算偏振空间中任意两点之间波动的重叠参数来识别特定波长的复制对称性破缺,而其他波长保持复制对称性行为。偏振空间中的部分复模对称性破缺是调制不稳定性和自相位调制相互竞争的结果。我们的研究结果建立了极化作为探测无序光子系统中复杂能量景观的天然平台。
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引用次数: 0
Comparative dynamics and normal form of nonlocal chemotaxis models with spatial average and top-hat kernels 具有空间平均核和顶帽核的非局部趋化模型的比较动力学和范式
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-31 DOI: 10.1016/j.chaos.2026.118011
Yehu Lv
This study conducts a comparative analysis of two nonlocal chemotaxis models: one incorporating a spatial average kernel and the other a top-hat kernel with a perception radius M. We investigate how taxis and kernel selection impact model dynamics, employing linear stability and bifurcation theory to characterize the conditions for pattern formation. Through numerical simulations, we illustrate how the chemotactic coefficient χ modulates the critical perception radius MT and the spatial wave number. The key contributions of this work are the proof of local existence and uniqueness for a classical solution to model (1.1), as well as the systematic derivation of an explicit normal form for the Turing bifurcation under periodic boundary conditions with a spatial average kernel. This normal form provides analytical insight into the stability and direction of the resulting inhomogeneous patterns. Our results demonstrate that the top-hat kernel supports richer spatiotemporal dynamics than the spatially averaged kernel, and that stronger chemotaxis tends to suppress pattern formation unless compensated by a larger sensing range.
本研究对两个非局部趋化性模型进行了比较分析:一个包含空间平均核,另一个包含感知半径为m的顶帽核。我们利用线性稳定性和分岔理论来表征模式形成的条件,研究趋化性和核选择如何影响模型动力学。通过数值模拟,我们说明了趋化系数χ如何调节临界感知半径MT和空间波数。本文的主要贡献是证明了模型(1.1)经典解的局部存在性和唯一性,以及系统地推导了具有空间平均核的周期边界条件下图灵分岔的显式范式。这种范式提供了对所得到的非均匀模式的稳定性和方向的分析性洞察。我们的研究结果表明,顶帽核比空间平均核支持更丰富的时空动态,并且除非通过更大的传感范围补偿,否则更强的趋化性倾向于抑制模式形成。
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引用次数: 0
Excitation and propagation of the high-order self-similar rogue waves in aircraft wing plates with nonlinear aeroelastic restraints 非线性气动弹性约束下飞机翼板高阶自相似异常波的激发与传播
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-31 DOI: 10.1016/j.chaos.2026.117985
Yi Fei Zhang , Wei Zhang , Yu Fei Zhang
This paper investigates the propagation mechanisms of the higher-order self-similar two-dimensional rogue waves in the aircraft wings modeled as the thin plates resting on the nonlinear elastic foundations. The nonlinear governing dynamic equation of motion is reduced to a (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation by the reductive perturbation. The analysis of the dispersion relation indicates that the presence of the initial pre-stress fundamentally alters the dispersion characteristics of the system, providing the conditions for wave localization. The expressions of the analytical solutions for the higher-order rogue waves are constructed based on a self-similar transformation. Furthermore, the nonlinear evolution characteristics of the rogue waves are revealed through numerical simulations, while the parameter analysis further demonstrates that the wave amplitude is sensitive to variations in the initial compressive stress, foundation nonlinear coefficient, and plate thickness. The results provide the theoretical support for the damage prevention and wave control in the aircraft wings under the extreme wave loads.
研究了高阶自相似二维异常波在基于非线性弹性基础的薄板飞机机翼中的传播机理。通过约化摄动将非线性运动控制动力学方程化为(2 + 1)维非线性Schrödinger (NLS)方程。色散关系分析表明,初始预应力的存在从根本上改变了系统的色散特性,为波的局部化提供了条件。基于自相似变换,构造了高阶异常波解析解的表达式。数值模拟揭示了异常波的非线性演化特征,参数分析进一步表明,异常波振幅对初始压应力、地基非线性系数和板厚的变化较为敏感。研究结果为飞机机翼在极端波浪荷载作用下的防损伤和控波提供了理论支持。
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引用次数: 0
The vanishing pressure limits in Riemann solutions for the non-isentropic Euler equations with combined pressure and time-dependent source term 具有压力和时间相关源项的非等熵欧拉方程的Riemann解中消失的压力极限
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-31 DOI: 10.1016/j.chaos.2026.118013
Tao Li, Yongqiang Fan
In this paper, we investigate the vanishing pressure limits of Riemann solutions for the one-dimensional (1-D) non-isentropic Euler equations with a time-dependent source term and a combined equation of state incorporating both polytropic and logarithmic terms. Since the right-hand side of equations contains a time-varying source term, the solutions of the Riemann problem lose self-similarity. To address this challenge, a velocity transformation is employed to convert the 1-D Euler system with a time-dependent source term into the conservation law form. Firstly, based on the characteristic analysis and phase plane analysis, Riemann solutions are obtained for the transformed conservative system, encompassing rarefaction wave, contact discontinuity, and shock wave. Subsequently, the Riemann solutions of the original system are derived by the velocity transformation. Furthermore, the limiting behavior of these Riemann solutions are studied as the pressure tends to zero. The analytical results demonstrate that the Riemann solutions of the original system, which consist of a 1-shock wave, a 3-shock wave, and a contact discontinuity, converge to the delta shock (δ-shock) wave solution of the pressureless Euler system with the same source term. The solutions composed of a 1-rarefaction wave, a 3-rarefaction wave, and a contact discontinuity, converge to the pressureless Euler system with a source term, involving the contact discontinuity and vacuum. Finally, some numerical examples are provided to show the formation of δ-shock wave and vacuum.
本文研究了具有时变源项和包含多向项和对数项的组合状态方程的一维(1-D)非等熵欧拉方程的Riemann解的消失压力极限。由于方程的右侧包含时变源项,黎曼问题的解失去了自相似性。为了解决这一挑战,采用速度变换将具有时间依赖源项的一维欧拉系统转换为守恒律形式。首先,基于特征分析和相平面分析,得到了变换后的包含稀薄波、接触不连续波和激波的保守系统的Riemann解;然后,通过速度变换导出了原系统的黎曼解。进一步研究了这些黎曼解在压力趋于零时的极限行为。分析结果表明,由1激波、3激波和接触不连续组成的原始系统的Riemann解收敛于具有相同源项的无压欧拉系统的δ激波解。由1稀薄波、3稀薄波和接触不连续组成的解收敛到包含接触不连续和真空的源项无压欧拉系统。最后,给出了δ激波和真空形成的数值例子。
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引用次数: 0
Q-switched and vector soliton pulses generation in an Er-doped fiber laser mode-locked by the PbSe-QDs saturable absorber 用PbSe-QDs饱和吸收体锁模的掺铒光纤激光器中q开关和矢量孤子脉冲的产生
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-31 DOI: 10.1016/j.chaos.2026.117921
Zefeng Wang , Daping Luo , Chaoyu Ning , Zhiwei Zhu , Xu Gao , Zhenning Xu , Zejiang Deng , Ruiguang Chang , Ling Zhang , Zhenghui Wu , Tianci Zhang , Chenglin Gu , Wenxue Li
PbSe quantum dots (QDs) have demonstrated excellent optical properties suitable for high-performance lasers and stable pulse generation. Here, we present an all-fiber laser cavity operating at 1.5-μm with a homemade sandwiched PbSe saturable absorber (SA), which enables stable high-energy pulses both in Q-switching and mode-locking operations. Notably, we report, for the first time, the generation of polarization-locked vector solitons (PLVSs) using a PbSe-QDs-based SA in the mode-locking regime. In the Q-switching operation, the repetition rate could be tuned from 12.48 kHz to 35.25 kHz by adjusting the pump power, yielding a maximum pulse energy of 208 nJ with a pulse width of 2.81 μs at the pump power of 183 mW. This represents the best performance reported to date for PbSe-QDs SAs. In the mode-locking regime, the PbSe-QDs SA also exhibited outstanding performance in generating ultrashort pulses, producing soliton pulses with a repetition rate of 28.51 MHz, an average output power of 26.80 mW, and a pulse duration of 673 fs. Further detailed characterization confirmed that these solitons are indeed PLVSs, marking the first realization of vector solitons with the PbSe-QDs SA. Moreover, the PbSe-QDs SA demonstrated excellent long-term stability in the constant mode locking over 6 h with a power fluctuation around 0.15%. These results highlight the exceptional optical properties of PbSe QDs and unambiguously imply the potential as a high-performance SA for applications in ultrafast optics, nonlinear photonics, optical modulators and related fields.
PbSe量子点(QDs)具有优异的光学性能,适合于高性能激光器和稳定的脉冲产生。在这里,我们提出了一个工作在1.5 μm的全光纤激光腔,其中含有自制的夹心PbSe可饱和吸收体(SA),可以在q开关和锁模操作中实现稳定的高能脉冲。值得注意的是,我们首次报道了在模式锁定机制下使用基于pbse - qds的SA产生偏振锁定矢量孤子(PLVSs)。在调q工作中,通过调节泵浦功率可将重复频率从12.48 kHz调到35.25 kHz,在泵浦功率为183 mW时,脉冲能量最大为208 nJ,脉冲宽度为2.81 μs。这代表了迄今为止报道的PbSe-QDs sa的最佳性能。在锁模模式下,PbSe-QDs SA在产生超短脉冲方面也表现出了出色的性能,产生的脉冲重复率为28.51 MHz,平均输出功率为26.80 mW,脉冲持续时间为673 fs。进一步的详细表征证实了这些孤子确实是PLVSs,标志着首次实现了具有PbSe-QDs SA的矢量孤子。此外,PbSe-QDs SA在6 h的恒定模式锁定中表现出良好的长期稳定性,功率波动约为0.15%。这些结果突出了PbSe量子点独特的光学特性,并明确暗示了作为高性能SA在超快光学、非线性光子学、光调制器和相关领域应用的潜力。
{"title":"Q-switched and vector soliton pulses generation in an Er-doped fiber laser mode-locked by the PbSe-QDs saturable absorber","authors":"Zefeng Wang ,&nbsp;Daping Luo ,&nbsp;Chaoyu Ning ,&nbsp;Zhiwei Zhu ,&nbsp;Xu Gao ,&nbsp;Zhenning Xu ,&nbsp;Zejiang Deng ,&nbsp;Ruiguang Chang ,&nbsp;Ling Zhang ,&nbsp;Zhenghui Wu ,&nbsp;Tianci Zhang ,&nbsp;Chenglin Gu ,&nbsp;Wenxue Li","doi":"10.1016/j.chaos.2026.117921","DOIUrl":"10.1016/j.chaos.2026.117921","url":null,"abstract":"<div><div>PbSe quantum dots (QDs) have demonstrated excellent optical properties suitable for high-performance lasers and stable pulse generation. Here, we present an all-fiber laser cavity operating at 1.5-μm with a homemade sandwiched PbSe saturable absorber (SA), which enables stable high-energy pulses both in Q-switching and mode-locking operations. Notably, we report, for the first time, the generation of polarization-locked vector solitons (PLVSs) using a PbSe-QDs-based SA in the mode-locking regime. In the Q-switching operation, the repetition rate could be tuned from 12.48 kHz to 35.25 kHz by adjusting the pump power, yielding a maximum pulse energy of 208 nJ with a pulse width of 2.81 μs at the pump power of 183 mW. This represents the best performance reported to date for PbSe-QDs SAs. In the mode-locking regime, the PbSe-QDs SA also exhibited outstanding performance in generating ultrashort pulses, producing soliton pulses with a repetition rate of 28.51 MHz, an average output power of 26.80 mW, and a pulse duration of 673 fs. Further detailed characterization confirmed that these solitons are indeed PLVSs, marking the first realization of vector solitons with the PbSe-QDs SA. Moreover, the PbSe-QDs SA demonstrated excellent long-term stability in the constant mode locking over 6 h with a power fluctuation around 0.15%. These results highlight the exceptional optical properties of PbSe QDs and unambiguously imply the potential as a high-performance SA for applications in ultrafast optics, nonlinear photonics, optical modulators and related fields.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"207 ","pages":"Article 117921"},"PeriodicalIF":5.6,"publicationDate":"2026-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adaptive neural network passivity-based control with state observer for partially unknown nonlinear systems 部分未知非线性系统的状态观测器自适应神经网络无源控制
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-30 DOI: 10.1016/j.chaos.2026.117989
Junjie Gong , Shengjie Guo , Jian Chen , Dengsheng Cai , Liang He , Wei Wei , Yu Long
To overcome the limitations of interconnection and damping assignment passivity-based control (IDA-PBC) in partially unknown nonlinear systems, particularly the reliance on large damping coefficients that may cause control inputs to exceed physical constraints, this paper proposes a novel adaptive neural network passivity-based control strategy incorporating a passivity-based observer. In the proposed framework, neural networks are introduced to relax the strict requirement of the desired closed-loop port-controlled Hamiltonian (PCH) model and to construct dynamic compensation mechanisms. These mechanisms are embedded into the interconnection and damping assignment passivity-based observer (IDA-PBO), resulting in an adaptive neural network IDA-PBO (ANNIDA-PBO) with enhanced dynamic compensation capability. On the control side, neural-network-based adaptive laws and compensation terms are developed to accurately approximate and compensate for unmodeled dynamics. This design alleviates the inherent limitation of conventional IDA-PBC methods that depend on large damping coefficients to achieve robustness. As a result, the proposed framework enables a well-conditioned selection of control gains within physical constraints and effectively decouples the strong dependence between robustness performance and damping parameters in standard IDA-PBC designs. Furthermore, the closed-loop system is shown to be semi-globally uniformly ultimately bounded through port-controlled Hamiltonian modeling and Lyapunov stability analysis. Finally, simulation studies on two representative nonlinear systems are conducted to validate the proposed method, demonstrating improved control accuracy and enhanced robustness against external disturbances.
为了克服部分未知非线性系统中基于互连和阻尼分配的无源控制(IDA-PBC)的局限性,特别是对可能导致控制输入超出物理约束的大阻尼系数的依赖,本文提出了一种新的基于无源观测器的自适应神经网络无源控制策略。在该框架中,引入神经网络,放宽了对理想的闭环端口控制哈密顿模型的严格要求,并构建了动态补偿机制。将这些机制嵌入到基于互联和阻尼分配的无源观测器(IDA-PBO)中,形成具有增强动态补偿能力的自适应神经网络IDA-PBO (ANNIDA-PBO)。在控制方面,开发了基于神经网络的自适应律和补偿项,以精确地逼近和补偿未建模的动力学。该设计减轻了传统IDA-PBC方法依赖大阻尼系数来实现鲁棒性的固有局限性。因此,所提出的框架能够在物理约束下进行条件良好的控制增益选择,并有效地解耦了标准IDA-PBC设计中鲁棒性性能与阻尼参数之间的强依赖性。进一步,通过端口控制哈密顿模型和Lyapunov稳定性分析,证明了闭环系统是半全局一致最终有界的。最后,对两个具有代表性的非线性系统进行了仿真研究,验证了所提方法的有效性,表明该方法提高了控制精度,增强了对外部干扰的鲁棒性。
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引用次数: 0
Predicting the onset of period-doubling bifurcations via dominant eigenvalue extracted from autocorrelation 利用自相关提取的优势特征值预测倍周期分岔的发生
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-30 DOI: 10.1016/j.chaos.2026.118010
Zhiqin Ma , Chunhua Zeng , Ting Gao , Jinqiao Duan
Predicting the occurrence of transitions in the qualitative dynamics of many natural systems is crucial, yet it remains a challenging task. Generic early warning signals like variance and lag-1 autocorrelation identify critical slowing down near tipping points but lack practical thresholds for predicting imminent transitions. More recent studies found that the dynamical eigenvalue is rooted in the framework of empirical dynamical modeling and then estimates the dominant eigenvalue of a system from time series, providing a threshold (|DEV| = 1) to predict bifurcations and classify their types. However, its application requires careful calibration of the hyperparameters and focuses on reconstructing system dynamics directly from data. Here, we employ Ornstein–Uhlenbeck process to derive analytic approximations for the lag-τ autocorrelation function prior to period-doubling bifurcation thereby estimating the dominant eigenvalue of dynamical systems, named dominant eigenvalue extracted from autocorrelation (DE-AC), and revealing its dynamic behavior when approaching a period-doubling bifurcation. Theoretically, dominant eigenvalue tends to 1 when the system approaches a period-doubling bifurcation. In particular, we evaluated DE-AC on simulation data from cardiac alternans model and on experimental data from chick heart aggregates undergoing a period-doubling bifurcation. DE-AC reliably detected the beginning of the cardiac arrhythmia (period-doubling bifurcation) in most cases. Moreover, it demonstrated superior sensitivity and specificity as an early warning signal compared to the three widely used indicators—variance, lag-1 autocorrelation, and dynamical eigenvalue. Our theoretical and empirical results suggest that DE-AC represents a quantitative measure for predicting the onset of potentially dangerous alternating rhythms in the heart. The ability to better infer, detect, and distinguish the nature of impending transitions in complex systems will help humans manage critical transitions in biological systems.
预测在许多自然系统的定性动力学转变的发生是至关重要的,但它仍然是一个具有挑战性的任务。通用的早期预警信号,如方差和lag-1自相关,可以识别临界点附近的关键减速,但缺乏预测即将发生的转变的实际阈值。最近的研究发现,动态特征值植根于经验动力学建模的框架,然后从时间序列中估计系统的主导特征值,提供一个阈值(|DEV| = 1)来预测分岔并对其类型进行分类。然而,它的应用需要仔细校准超参数,并侧重于直接从数据重建系统动力学。本文采用Ornstein-Uhlenbeck过程推导了倍周期分岔前lag-τ自相关函数的解析近似,从而估计了动力系统的显性特征值,称为从自相关中提取的显性特征值(DE-AC),并揭示了其在接近倍周期分岔时的动态行为。理论上,当系统接近倍周期分岔时,优势特征值趋向于−1。特别是,我们在心脏交替模型的模拟数据和鸡心脏聚合体经历倍期分叉的实验数据上评估了DE-AC。DE-AC在大多数病例中可靠地检测到心律失常(双周期分叉)的开始。此外,与方差、lag-1自相关和动态特征值这三种广泛使用的指标相比,它作为预警信号表现出更高的灵敏度和特异性。我们的理论和实证结果表明,DE-AC代表了预测心脏潜在危险交替节律发作的定量措施。更好地推断、检测和区分复杂系统中即将发生的转变的性质的能力将有助于人类管理生物系统中的关键转变。
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引用次数: 0
Stabilization of fractional parabolic equations through designed robust Robin boundary controller 基于鲁棒Robin边界控制器的分数阶抛物方程镇定
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-30 DOI: 10.1016/j.chaos.2026.118003
Hassen Arfaoui
The paper deals with the boundary stabilization for time-fractional parabolic equations (TFPEs) with non-constant coefficients and distributed disturbance by backstepping approach. Firstly, boundary stabilization is investigated through right Robin boundary control (RRBC) with homogeneous left Robin boundary condition at the lower end of the spatial domain. In this context, we proved a Mittag-Leffler stability result for the solution of the TFPEs. To achieve this objective, a robust boundary feedback control law has been designed for the stabilization of the TFPEs by backstepping approach. To the best of our knowledge, the stabilization of TFPEs with left homogeneous Robin boundary condition through right Robin-type boundary feedback control law via backstepping method is novel. Some numerical examples are presented at the end of this paper to confirm the theoretical results.
本文用反步法研究了具有非常系数和分布扰动的时间分数型抛物方程的边界镇定问题。首先,利用空间域下端齐次左罗宾边界条件的右罗宾边界控制(RRBC)研究边界稳定问题;在这种情况下,我们证明了tpes解的Mittag-Leffler稳定性结果。为了实现这一目标,设计了一种鲁棒的边界反馈控制律,并采用回溯法实现了tfp的镇定。据我们所知,利用右罗宾型边界反馈控制律反步法稳定具有左齐次罗宾边界条件的TFPEs是一种新颖的方法。最后给出了一些数值算例来验证理论结果。
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引用次数: 0
Limit cycles of planar discontinuous piecewise linear Hamiltonian systems in three regions of Y-type 平面间断分段线性哈密顿系统在y型三区域上的极限环
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-01-30 DOI: 10.1016/j.chaos.2026.117997
Jaume Llibre , Regilene Oliveira
In recent years there has been a significant interest in studying discontinuous piecewise differential systems, mainly due to the wide range of applications in modeling natural phenomena. To understand the dynamics of these systems in the plane one challenge is to control their number of limit cycles. In this paper we study the existence of limit cycles in planar discontinuous piecewise linear Hamiltonian systems with three zones separated by the line Y={(x,y):x0andy=0}{(x,y):x=0andy0}{(x,y):x0andy=0}. We provide the maximum number of crossing limit cycles intersecting each branch of Y in one point, and intersecting two branches of the Y each one in two points. So we have solved the extension of the 16th Hilbert problem to this class of differential systems.
近年来,研究不连续分段微分系统引起了极大的兴趣,这主要是由于它在模拟自然现象方面的广泛应用。要理解这些系统在平面上的动力学,一个挑战是控制它们的极限环数。本文研究了平面不连续分段线性哈密顿系统极限环的存在性,该系统的三个区域由直线Y={(x, Y):x≥0andy=0}∪{(x, Y):x=0andy≥0}∪{(x, Y):x≤0andy=0}分隔。我们给出了与Y的每个分支相交于一点的最大极限环数,以及与Y的两个分支相交于两点的最大极限环数。我们已经解决了第16个希尔伯特问题对这类微分系统的推广。
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引用次数: 0
期刊
Chaos Solitons & Fractals
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