Pub Date : 2025-12-15DOI: 10.1016/j.chaos.2025.117775
Yanjuan Zhang , Yihan Gao , Yuting Wang , Chun Yang , Xiaoyang Liu , Wei Wang
Higher-order interactions can trigger abrupt, unpredictable epidemics, while individual awareness offers a potential line of defense. However, how these two forces coevolve to shape epidemic outcomes remains largely unexplored. Here, we bridge this gap by proposing a coevolutionary framework where disease spreads through both pairwise and group interactions on simplicial complexes, while individual risk perception dynamically modulates transmission probabilities. To unravel the system’s complex behavior, we develop a novel degree-weighted dimension-reduction approach that condenses the high-dimensional dynamics into a single, accurate effective equation. Our analysis reveals a powerful counterbalance: while higher-order mechanisms lower the epidemic invasion threshold, risk perception significantly raises it. Most strikingly, we find that sufficiently strong awareness can fundamentally alter the nature of the epidemic transition, eliminating the catastrophic discontinuous phase transition typical of higher-order systems and restoring a smooth, continuous response. This conclusion holds across both artificial and real-world networks. These results demonstrate that awareness is not merely a secondary factor but a critical control lever that can tame the inherent instability of higher-order contagion. Our work provides a quantitative framework for designing more effective, behavior-aware interventions to mitigate the risk of sudden outbreaks in our increasingly complex social world.
{"title":"Awareness tames abrupt transitions in higher-order epidemics","authors":"Yanjuan Zhang , Yihan Gao , Yuting Wang , Chun Yang , Xiaoyang Liu , Wei Wang","doi":"10.1016/j.chaos.2025.117775","DOIUrl":"10.1016/j.chaos.2025.117775","url":null,"abstract":"<div><div>Higher-order interactions can trigger abrupt, unpredictable epidemics, while individual awareness offers a potential line of defense. However, how these two forces coevolve to shape epidemic outcomes remains largely unexplored. Here, we bridge this gap by proposing a coevolutionary framework where disease spreads through both pairwise and group interactions on simplicial complexes, while individual risk perception dynamically modulates transmission probabilities. To unravel the system’s complex behavior, we develop a novel degree-weighted dimension-reduction approach that condenses the high-dimensional dynamics into a single, accurate effective equation. Our analysis reveals a powerful counterbalance: while higher-order mechanisms lower the epidemic invasion threshold, risk perception significantly raises it. Most strikingly, we find that sufficiently strong awareness can fundamentally alter the nature of the epidemic transition, eliminating the catastrophic discontinuous phase transition typical of higher-order systems and restoring a smooth, continuous response. This conclusion holds across both artificial and real-world networks. These results demonstrate that awareness is not merely a secondary factor but a critical control lever that can tame the inherent instability of higher-order contagion. Our work provides a quantitative framework for designing more effective, behavior-aware interventions to mitigate the risk of sudden outbreaks in our increasingly complex social world.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117775"},"PeriodicalIF":5.6,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784746","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}
Pub Date : 2025-12-15DOI: 10.1016/j.chaos.2025.117679
Wenyu Yang , Baofeng Sun , Guodong Ma , Huijun Sun
With the increasing number of regular vehicles obtaining real-time traffic information through mobile applications, many are gradually evolving into connected human-driven vehicles (CHVs). Most existing studies focus on modeling the impact of continuous information in driver assistance systems. However, they often overlook advanced event-triggered information, which can strongly influence drivers' decision-making. This limitation significantly restricts the ability of existing models to capture realistic CHV behavior. To address this issue, this study proposes a CHV car-following model framework capable of responding to multiple types of driver assistance information. The framework is built on two sub-models. The first sub-model, developed under the dual-process theory, responds to continuous information and captures drivers' dynamic compliance rate under perceived risk. The second sub-model responds to advanced event-triggered information and describes drivers' behavioral reactions when emergency messages are received from the cloud control platform. Based on this model, linear and nonlinear stability analyses are conducted to investigate the effects of different delay sources on CHV traffic flow stability. The analyses are performed after eliminating the approximation errors arising from delay simplifications in existing methods. The results show that the driver reaction delay remains the dominant factor influencing string stability. When the driver reaction delay stays within the normal range, maintaining the connected vehicle communication delay below a reasonable threshold can significantly enhance traffic flow stability. In addition, the maximum compliance rate, together with the various delay levels, jointly determines the stability boundary of the traffic flow. Based on these findings, several design recommendations for driver assistance systems are proposed to achieve a coordinated balance among efficiency, safety, and cost in connected traffic environments.
{"title":"Car-following modeling with multi-model driving assistance and stability analysis under heterogeneous time delay","authors":"Wenyu Yang , Baofeng Sun , Guodong Ma , Huijun Sun","doi":"10.1016/j.chaos.2025.117679","DOIUrl":"10.1016/j.chaos.2025.117679","url":null,"abstract":"<div><div>With the increasing number of regular vehicles obtaining real-time traffic information through mobile applications, many are gradually evolving into connected human-driven vehicles (CHVs). Most existing studies focus on modeling the impact of continuous information in driver assistance systems. However, they often overlook advanced event-triggered information, which can strongly influence drivers' decision-making. This limitation significantly restricts the ability of existing models to capture realistic CHV behavior. To address this issue, this study proposes a CHV car-following model framework capable of responding to multiple types of driver assistance information. The framework is built on two sub-models. The first sub-model, developed under the dual-process theory, responds to continuous information and captures drivers' dynamic compliance rate under perceived risk. The second sub-model responds to advanced event-triggered information and describes drivers' behavioral reactions when emergency messages are received from the cloud control platform. Based on this model, linear and nonlinear stability analyses are conducted to investigate the effects of different delay sources on CHV traffic flow stability. The analyses are performed after eliminating the approximation errors arising from delay simplifications in existing methods. The results show that the driver reaction delay remains the dominant factor influencing string stability. When the driver reaction delay stays within the normal range, maintaining the connected vehicle communication delay below a reasonable threshold can significantly enhance traffic flow stability. In addition, the maximum compliance rate, together with the various delay levels, jointly determines the stability boundary of the traffic flow. Based on these findings, several design recommendations for driver assistance systems are proposed to achieve a coordinated balance among efficiency, safety, and cost in connected traffic environments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117679"},"PeriodicalIF":5.6,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145759468","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}
Pub Date : 2025-12-15DOI: 10.1016/j.chaos.2025.117622
Mijat Paunović , Marko Ćosić , Nikola N. Radovanović , Mirjana M. Platiša , Nadica Miljković
Objectives
We propose an improvement to our novel approach for Heart Rate Asymmetry (HRA) assessment based on Poincaré Plots (PPs) derived from Heart Rate Variability (HRV). We evaluate the ability of the modified Asymmetry Magnitude Index (AMI) to discriminate between clinically distinct cohorts and its applicability to short-term HRV.
Methods
For both AMI variants, the degree of asymmetry is quantified by applying the Frobenius norm to the Asymmetric Matrix Component (AMC) of an estimated two-dimensional PP distribution. The approaches differ only in the estimation method, with the modified AMI using Kernel Density Estimation (KDE) method instead of square histograms. The KDE AMI is compared with the Histogram-based counterpart (HB AMI), standardized PP descriptors, and established HRA measures using 20-minute HRV from healthy subjects (HS) and patients with Congestive Heart Failure (CHF), as well as segments of 1, 5, and 10 min.
Results
The KDE AMI and standardized PP descriptor SD1 outperform other measures, distinguishing older HS vs. patients with CHF (oHS vs. CHF) and younger vs. older healthy subgroups (yHS vs. oHS), irrespective of HRV duration. In contrast, the HB AMI and SD2 perform well only at longer timescales for oHS vs. CHF, while offering similar discrimination for yHS vs. oHS. Other HRA indices reach statistical significance only at specific timescales.
Conclusions
KDE AMI successfully detects differences in HRA between clinically distinct cohorts. The discriminative power of KDE AMI is comparable to that of SD1, whereas among HRA measures, it demonstrates the strongest and most consistent performance across short-term timescales. Moreover, the results justify the rationale for the employment of KDE to address the limitations of the Histogram-based counterpart. Further refinement and validation of the proposed index could pave the way for its seamless integration into routine clinical practice and wearable technologies. To strengthen its applicability, current limitations should be addressed by evaluating the index across a more diverse patient sample.
目的对基于心率变异性（HRV）得出的poincar图（PPs）的心率不对称（HRA）评估方法进行改进。我们评估改良的不对称幅度指数（AMI）区分临床不同队列的能力及其对短期HRV的适用性。方法通过对估计的二维PP分布的不对称矩阵分量（AMC）应用Frobenius范数，对两种AMI变体的不对称程度进行量化。这两种方法仅在估计方法上有所不同，改进的AMI使用核密度估计（KDE）方法而不是方形直方图。KDE AMI与基于直方图的对应物（HB AMI）、标准化PP描述符以及使用健康受试者（HS）和充血性心力衰竭（CHF）患者的20分钟HRV以及1、5和10分钟片段建立的HRA测量进行比较。结果KDE AMI和标准化PP描述符SD1优于其他测量，区分老年HS与CHF患者（oHS vs. CHF）和年轻与老年健康亚组（yHS vs. oHS），与HRV持续时间无关。相比之下，HB AMI和SD2仅在较长的时间尺度上对oHS和CHF表现良好，而对yHS和oHS也有类似的区别。其他HRA指标仅在特定的时间尺度上才具有统计学意义。结论kde AMI成功地检测出临床不同队列之间HRA的差异。KDE AMI的判别能力与SD1相当，而在HRA测量中，它在短期时间尺度上表现出最强和最一致的性能。此外，结果证明了使用KDE来解决基于直方图的对应物的局限性的基本原理。该指数的进一步完善和验证可以为其与常规临床实践和可穿戴技术的无缝集成铺平道路。为了加强其适用性，应通过在更多样化的患者样本中评估该指数来解决当前的局限性。
{"title":"Mapping the heart rhythm: Leveraging Poincaré plot asymmetry to detect congestive heart failure and age-related changes","authors":"Mijat Paunović , Marko Ćosić , Nikola N. Radovanović , Mirjana M. Platiša , Nadica Miljković","doi":"10.1016/j.chaos.2025.117622","DOIUrl":"10.1016/j.chaos.2025.117622","url":null,"abstract":"<div><h3>Objectives</h3><div>We propose an improvement to our novel approach for Heart Rate Asymmetry (HRA) assessment based on Poincaré Plots (PPs) derived from Heart Rate Variability (HRV). We evaluate the ability of the modified Asymmetry Magnitude Index (AMI) to discriminate between clinically distinct cohorts and its applicability to short-term HRV.</div></div><div><h3>Methods</h3><div>For both AMI variants, the degree of asymmetry is quantified by applying the Frobenius norm to the Asymmetric Matrix Component (AMC) of an estimated two-dimensional PP distribution. The approaches differ only in the estimation method, with the modified AMI using Kernel Density Estimation (KDE) method instead of square histograms. The KDE AMI is compared with the Histogram-based counterpart (HB AMI), standardized PP descriptors, and established HRA measures using 20-minute HRV from healthy subjects (HS) and patients with Congestive Heart Failure (CHF), as well as segments of 1, 5, and 10 min.</div></div><div><h3>Results</h3><div>The KDE AMI and standardized PP descriptor SD1 outperform other measures, distinguishing older HS vs. patients with CHF (oHS vs. CHF) and younger vs. older healthy subgroups (yHS vs. oHS), irrespective of HRV duration. In contrast, the HB AMI and SD2 perform well only at longer timescales for oHS vs. CHF, while offering similar discrimination for yHS vs. oHS. Other HRA indices reach statistical significance only at specific timescales.</div></div><div><h3>Conclusions</h3><div>KDE AMI successfully detects differences in HRA between clinically distinct cohorts. The discriminative power of KDE AMI is comparable to that of SD1, whereas among HRA measures, it demonstrates the strongest and most consistent performance across short-term timescales. Moreover, the results justify the rationale for the employment of KDE to address the limitations of the Histogram-based counterpart. Further refinement and validation of the proposed index could pave the way for its seamless integration into routine clinical practice and wearable technologies. To strengthen its applicability, current limitations should be addressed by evaluating the index across a more diverse patient sample.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117622"},"PeriodicalIF":5.6,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784747","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}
Pub Date : 2025-12-15DOI: 10.1016/j.chaos.2025.117764
Yi-peng Hu , Qian-ming Ding , Yong Wu , Dong Yu , Tian-yu Li , Ya Jia
Spiral wave is a phenomenon widely observed in excitable media. Defects in cardiac tissue can induce the pinning of spiral waves, leading to arrhythmias. Although electrical defibrillation can restore normal rhythm, it demands high energy and inflicts substantial tissue damage. Optogenetics offers a low-energy alternative, yet the optical energy deposited in tissue inevitably converts to heat, which can undermine efficacy and introduce new safety concerns. This letter proposes a novel strategy based on the Dynamic Learning Synchronization method (DLS-ADMM), utilizing the background of optogenetics to effectively unpin the spiral wave through adaptive light intensity. Our method successfully unpinned and eliminated spiral waves by adaptively adjustment of the light intensity in different defects. Compared with the conventional constant-illumination approach, spiral waves can be unpinned and eliminated by DLS-ADMM at lower light intensity, enabling the low-energy control. This work provides an algorithmic framework and theoretical basis for developing efficient, low-energy defibrillation techniques.
{"title":"Unpinning and elimination of spiral waves: A machine learning-based method","authors":"Yi-peng Hu , Qian-ming Ding , Yong Wu , Dong Yu , Tian-yu Li , Ya Jia","doi":"10.1016/j.chaos.2025.117764","DOIUrl":"10.1016/j.chaos.2025.117764","url":null,"abstract":"<div><div>Spiral wave is a phenomenon widely observed in excitable media. Defects in cardiac tissue can induce the pinning of spiral waves, leading to arrhythmias. Although electrical defibrillation can restore normal rhythm, it demands high energy and inflicts substantial tissue damage. Optogenetics offers a low-energy alternative, yet the optical energy deposited in tissue inevitably converts to heat, which can undermine efficacy and introduce new safety concerns. This letter proposes a novel strategy based on the Dynamic Learning Synchronization method (DLS-ADMM), utilizing the background of optogenetics to effectively unpin the spiral wave through adaptive light intensity. Our method successfully unpinned and eliminated spiral waves by adaptively adjustment of the light intensity in different defects. Compared with the conventional constant-illumination approach, spiral waves can be unpinned and eliminated by DLS-ADMM at lower light intensity, enabling the low-energy control. This work provides an algorithmic framework and theoretical basis for developing efficient, low-energy defibrillation techniques.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117764"},"PeriodicalIF":5.6,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784742","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}
Pub Date : 2025-12-14DOI: 10.1016/j.chaos.2025.117770
Hai-Dong Qu, Xuan Liu, Xiao-peng Yang
This paper develops a Legendre interpolation method (LIM) for solving initial–boundary value problems of nonlinear variable-order fractional advection–diffusion equations with two-sided derivatives. The proposed approach combines a Crank–Nicolson temporal discretization with spatial approximation using shifted Legendre polynomials. We establish comprehensive stability and convergence analyses for both semi-discrete and fully discrete schemes, proving second-order temporal convergence and exponential spatial convergence. Numerical experiments validate the theoretical findings and demonstrate the method’s high accuracy across various test cases, including nonlinear problems with variable coefficients. The method effectively handles complex variable-order fractional operators while maintaining computational efficiency through optimized matrix structures.
{"title":"A Legendre interpolation method for the nonlinear variable-order fractional advection–diffusion equations","authors":"Hai-Dong Qu, Xuan Liu, Xiao-peng Yang","doi":"10.1016/j.chaos.2025.117770","DOIUrl":"10.1016/j.chaos.2025.117770","url":null,"abstract":"<div><div>This paper develops a Legendre interpolation method (LIM) for solving initial–boundary value problems of nonlinear variable-order fractional advection–diffusion equations with two-sided derivatives. The proposed approach combines a Crank–Nicolson temporal discretization with spatial approximation using shifted Legendre polynomials. We establish comprehensive stability and convergence analyses for both semi-discrete and fully discrete schemes, proving second-order temporal convergence and exponential spatial convergence. Numerical experiments validate the theoretical findings and demonstrate the method’s high accuracy across various test cases, including nonlinear problems with variable coefficients. The method effectively handles complex variable-order fractional operators while maintaining computational efficiency through optimized matrix structures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117770"},"PeriodicalIF":5.6,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145759477","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}
Pub Date : 2025-12-14DOI: 10.1016/j.chaos.2025.117763
Peng Chen , Jieqing Tan , Yangang Yao , Yan Xing , Yan Yao
This article explores the tracking control problem for strict-feedback multi-input multi-output (MIMO) nonlinear systems subject to deferred asymmetric output constraints, in the case where the reference signals are discontinuous. It strives not only to achieve discontinuous reference tracking without constraint violation, but also to actively damp error oscillations induced by external disturbances, unmodelled dynamics, and high-frequency references. The existing studies are limited to single-input single-output nonlinear systems, MIMO nonlinear systems with strong controllability conditions, or systems with available nonlinearities or reference derivatives. To overcome these limitations, a novel global low-complexity hybrid tracking control scheme consisting of a mixed-gain funnel constrained (FC) controller and a proportional-integral (PI) controller is put forward in this article. It retains the inherent simplicity of FC control and PI control, requiring neither function approximation, parameter identification, command filtering, nor disturbance estimation. Moreover, by inserting a shifting function and two parameters into the controllers, the proposed scheme helps alleviate the initial control peaking and enhances the transient performance of tracking errors. A two-link robotic manipulator example is provided to demonstrate the reliability of the developed control algorithm.
{"title":"Global low-complexity hybrid tracking control of MIMO nonlinear systems with discontinuous references","authors":"Peng Chen , Jieqing Tan , Yangang Yao , Yan Xing , Yan Yao","doi":"10.1016/j.chaos.2025.117763","DOIUrl":"10.1016/j.chaos.2025.117763","url":null,"abstract":"<div><div>This article explores the tracking control problem for strict-feedback multi-input multi-output (MIMO) nonlinear systems subject to deferred asymmetric output constraints, in the case where the reference signals are discontinuous. It strives not only to achieve discontinuous reference tracking without constraint violation, but also to actively damp error oscillations induced by external disturbances, unmodelled dynamics, and high-frequency references. The existing studies are limited to single-input single-output nonlinear systems, MIMO nonlinear systems with strong controllability conditions, or systems with available nonlinearities or reference derivatives. To overcome these limitations, a novel global low-complexity hybrid tracking control scheme consisting of a mixed-gain funnel constrained (FC) controller and a proportional-integral (PI) controller is put forward in this article. It retains the inherent simplicity of FC control and PI control, requiring neither function approximation, parameter identification, command filtering, nor disturbance estimation. Moreover, by inserting a shifting function and two parameters into the controllers, the proposed scheme helps alleviate the initial control peaking and enhances the transient performance of tracking errors. A two-link robotic manipulator example is provided to demonstrate the reliability of the developed control algorithm.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117763"},"PeriodicalIF":5.6,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145759496","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}
Pub Date : 2025-12-13DOI: 10.1016/j.chaos.2025.117756
Shin-ichi Inage
The present study investigates the spectral behavior of temperature fluctuations in homogeneous isotropic turbulence at low Prandtl numbers using an extended GOY shell model that incorporates a passive-scalar field. The model enables simultaneous computation of the velocity and temperature dynamics and reveals a unified picture linking the inertial-convective and dissipation ranges. Numerical results demonstrate that the apparent “long-tail” behavior of the temperature fluctuation spectrum at low Prandtl numbers does not arise from delayed diffusion but from a scale effect associated with the reduction of the scalar-dissipation wavenumber . By applying nondimensional variables and , spectra obtained under various Reynolds and Prandtl numbers collapse onto a single curve, confirming a universal transition at from the inertial-convective to the diffusion-dominated regime. Extending the Hebishima–Inage exponential spectrum, an empirical expression with the fitted correlation reproduces the shell-model results quantitatively over the entire wavenumber range. The findings establish a coherent theoretical framework for passive-scalar turbulence and provide a foundation for modeling thermal transport and mixing in low-Prandtl-number fluids such as liquid metals and plasma flows.
{"title":"Spectral behavior of low-Prandtl-number temperature fluctuations in isotropic turbulence: Insights from a GOY shell model","authors":"Shin-ichi Inage","doi":"10.1016/j.chaos.2025.117756","DOIUrl":"10.1016/j.chaos.2025.117756","url":null,"abstract":"<div><div>The present study investigates the spectral behavior of temperature fluctuations in homogeneous isotropic turbulence at low Prandtl numbers using an extended GOY shell model that incorporates a passive-scalar field. The model enables simultaneous computation of the velocity and temperature dynamics and reveals a unified picture linking the inertial-convective and dissipation ranges. Numerical results demonstrate that the apparent “long-tail” behavior of the temperature fluctuation spectrum at low Prandtl numbers does not arise from delayed diffusion but from a scale effect associated with the reduction of the scalar-dissipation wavenumber <span><math><msub><mi>k</mi><mi>κ</mi></msub><mo>=</mo><msup><mfenced><mrow><mi>ε</mi><mo>/</mo><msup><mi>κ</mi><mn>3</mn></msup></mrow></mfenced><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup></math></span>. By applying nondimensional variables <span><math><msup><mi>k</mi><mo>∗</mo></msup><mo>=</mo><mi>k</mi><mo>/</mo><msub><mi>k</mi><mi>κ</mi></msub></math></span> and <span><math><msubsup><mi>E</mi><mi>θ</mi><mo>∗</mo></msubsup><mfenced><msup><mi>k</mi><mo>∗</mo></msup></mfenced><mo>=</mo><msub><mi>E</mi><mi>θ</mi></msub><mfenced><mi>k</mi></mfenced><mo>/</mo><mfenced><mrow><mfenced><mrow><mi>χ</mi><mo>/</mo><msup><mi>ε</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></mfenced><msubsup><mi>k</mi><mi>κ</mi><mrow><mo>−</mo><mn>5</mn><mo>/</mo><mn>3</mn></mrow></msubsup></mrow></mfenced></math></span>, spectra obtained under various Reynolds and Prandtl numbers collapse onto a single curve, confirming a universal transition at <span><math><msup><mi>k</mi><mo>∗</mo></msup><mo>≃</mo><mn>1</mn></math></span> from the inertial-convective to the diffusion-dominated regime. Extending the Hebishima–Inage exponential spectrum, an empirical expression <span><math><msub><mi>E</mi><mi>θ</mi></msub><mfenced><mi>k</mi></mfenced><mo>∝</mo><msup><mi>k</mi><mrow><mo>−</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></mrow></msup><mspace></mspace><mi>exp</mi><mfenced><mrow><mo>−</mo><mn>2.37</mn><msup><mfenced><mrow><mi>k</mi><mo>/</mo><msub><mi>k</mi><mi>κ</mi></msub></mrow></mfenced><msub><mi>α</mi><mi>θ</mi></msub></msup></mrow></mfenced></math></span> with the fitted correlation <span><math><msub><mi>α</mi><mi>θ</mi></msub><mo>=</mo><mn>0.5116</mn><msup><mi>Pr</mi><mn>3</mn></msup><mo>−</mo><mn>1.565</mn><msup><mi>Pr</mi><mn>2</mn></msup><mo>+</mo><mn>1.6802</mn><mi>Pr</mi><mo>+</mo><mn>0.8692</mn></math></span> reproduces the shell-model results quantitatively over the entire wavenumber range. The findings establish a coherent theoretical framework for passive-scalar turbulence and provide a foundation for modeling thermal transport and mixing in low-Prandtl-number fluids such as liquid metals and plasma flows.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117756"},"PeriodicalIF":5.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145759469","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}
Pub Date : 2025-12-13DOI: 10.1016/j.chaos.2025.117760
Jia-Jie Qin , Xinrui Ji , Mingze Qi , Gang Yan , Xiaozhu Zhang
Accurately characterizing the state of complex networked dynamical systems is crucial for understanding, prediction, and control of the systems, yet often hindered by the inaccessibility of the states of all nodes in the system. In this work, we introduce centrality-guided node selection strategies, enabling precise approximation of the system-wide average state based on the states of the selected nodes. Remarkably, our approach harnesses solely the structural information of the underlying network and does not require knowledge of the detailed node dynamics. Comprehensive simulations on various empirical networks and dynamic models demonstrate that eigenvector centrality, in particular, offers a robust choice. It yields node collections that reliably capture the global system state with exceptionally low errors, outperforming known strategies based on other measures across interaction topologies, network dynamics, sizes of the observed node set, and different regimes of systems’ dynamics in the parameter space. This work therefore provides a structure-based node selection strategy for efficient and accurate estimations of the global state of complex networked dynamical systems.
{"title":"Structure-based node selection for capturing complex system states","authors":"Jia-Jie Qin , Xinrui Ji , Mingze Qi , Gang Yan , Xiaozhu Zhang","doi":"10.1016/j.chaos.2025.117760","DOIUrl":"10.1016/j.chaos.2025.117760","url":null,"abstract":"<div><div>Accurately characterizing the state of complex networked dynamical systems is crucial for understanding, prediction, and control of the systems, yet often hindered by the inaccessibility of the states of all nodes in the system. In this work, we introduce centrality-guided node selection strategies, enabling precise approximation of the system-wide average state based on the states of the selected nodes. Remarkably, our approach harnesses solely the structural information of the underlying network and does not require knowledge of the detailed node dynamics. Comprehensive simulations on various empirical networks and dynamic models demonstrate that eigenvector centrality, in particular, offers a robust choice. It yields node collections that reliably capture the global system state with exceptionally low errors, outperforming known strategies based on other measures across interaction topologies, network dynamics, sizes of the observed node set, and different regimes of systems’ dynamics in the parameter space. This work therefore provides a structure-based node selection strategy for efficient and accurate estimations of the global state of complex networked dynamical systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117760"},"PeriodicalIF":5.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731393","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}
In a network attack environment, this paper investigates the data-driven modeling and fault estimation for a class of Lipschitz nonlinear systems with actuator and sensor faults. Here, the sampled measured output data from the system transmitted over the wireless network, which may pose a risk of being subjected to network attacks, can be captured by the receiving end. A checksum-redundancy correction based anti-attack strategy, which can restore the transmitted data to the original one, is proposed to ensure data reliability. A reliable data-driven differential equation model based observer associated with the original system is constructed, so as to achieve the estimation of system multi faults. LMI-based uniformly ultimate boundedness (UUB) stability conditions are proposed for the error dynamics. Then, an iterative observer related to the original system is designed to further improve the multi-fault estimation accuracy. A convergence theorem is given to guarantee the effectiveness of the designed iterative observer. Finally, a longitudinal dynamics model of the aircraft is exhibited to test the proposed strategy.
{"title":"Data-driven modeling and fault estimation for nonlinear systems: A checksum-redundancy correction based anti-attack strategy","authors":"Lu-Yao Dang, Sheng-Juan Huang, Liang-Dong Guo, Da-Qing Zhang, Li-Bing Wu","doi":"10.1016/j.chaos.2025.117768","DOIUrl":"10.1016/j.chaos.2025.117768","url":null,"abstract":"<div><div>In a network attack environment, this paper investigates the data-driven modeling and fault estimation for a class of Lipschitz nonlinear systems with actuator and sensor faults. Here, the sampled measured output data from the system transmitted over the wireless network, which may pose a risk of being subjected to network attacks, can be captured by the receiving end. A checksum-redundancy correction based anti-attack strategy, which can restore the transmitted data to the original one, is proposed to ensure data reliability. A reliable data-driven differential equation model based observer associated with the original system is constructed, so as to achieve the estimation of system multi faults. LMI-based uniformly ultimate boundedness (UUB) stability conditions are proposed for the error dynamics. Then, an iterative observer related to the original system is designed to further improve the multi-fault estimation accuracy. A convergence theorem is given to guarantee the effectiveness of the designed iterative observer. Finally, a longitudinal dynamics model of the aircraft is exhibited to test the proposed strategy.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117768"},"PeriodicalIF":5.6,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731392","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}
Pub Date : 2025-12-12DOI: 10.1016/j.chaos.2025.117761
Pshtiwan Othman Mohammed , Meraa Arab
The paper introduces a novel comparison technique for fractional difference equations of delta-type, which is used to establish sharp criteria for the asymptotic behavior of their solutions. It is demonstrated that the Mittag-Leffler function emerges as the unique solution to a specific case of the proposed model. In addition, using the comparison theorem, we derive precise conditions under which solutions either diverge to infinity or converge to zero. These theoretical results provide a robust framework for analyzing the long-term dynamics of discrete fractional systems. Finally, to verify the main theorems numerically and demonstrate their practical implications, four illustrative examples are presented.
{"title":"Asymptotic behavior and a new comparison technique for solutions of delta fractional difference equations","authors":"Pshtiwan Othman Mohammed , Meraa Arab","doi":"10.1016/j.chaos.2025.117761","DOIUrl":"10.1016/j.chaos.2025.117761","url":null,"abstract":"<div><div>The paper introduces a novel comparison technique for fractional difference equations of delta-type, which is used to establish sharp criteria for the asymptotic behavior of their solutions. It is demonstrated that the Mittag-Leffler function emerges as the unique solution to a specific case of the proposed model. In addition, using the comparison theorem, we derive precise conditions under which solutions either diverge to infinity or converge to zero. These theoretical results provide a robust framework for analyzing the long-term dynamics of discrete fractional systems. Finally, to verify the main theorems numerically and demonstrate their practical implications, four illustrative examples are presented.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117761"},"PeriodicalIF":5.6,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731675","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}
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