Chaos Solitons & Fractals最新文献_第7页

A systematic comparative analysis of modeling methods and variable-dependent weight optimization strategy for PINNs 系统比较分析了pinn的建模方法和变相关权重优化策略

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-27 DOI: 10.1016/j.chaos.2026.118163

Jie Yang , Jing Peng , Yasir Ramzan , Sanyi Tang , Jie Lou

{"title":"A systematic comparative analysis of modeling methods and variable-dependent weight optimization strategy for PINNs","authors":"Jie Yang , Jing Peng , Yasir Ramzan , Sanyi Tang , Jie Lou","doi":"10.1016/j.chaos.2026.118163","DOIUrl":"10.1016/j.chaos.2026.118163","url":null,"abstract":"<div><div>Dengue fever is a mosquito-borne infectious disease that poses a significant threat to public health and safety. It is crucial to establish the most appropriate mathematical model and estimate the most reliable parameters to simulate the epidemic and quantify control measures. Therefore, an ODE model, a FDE model and a discrete model are constructed. Three parameter estimation methods (PINNs/fPINNs/Euler-PINNs) are applied to three models (ODE/FDE/discrete), respectively, with data in Singapore. Specifically, a variable-dependent weight optimization strategy (VDWOS) for the inverse problem is newly proposed in this paper, which is compared with the traditional weight optimization strategy (TWOS). For theoretical analysis, there are essential differences: when the endemic equilibrium of the ODE/FDE model is globally asymptotically stable, the discrete model may exhibit a flip bifurcation, resulting in a disruption of stability. For numerical simulation, by comparing TWOS and VDWOS for three models, VDWOS yields more reliable parameters and time-varying parameter <span><math><mrow><mi>β</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> without specific function assumptions. Furthermore, an LSTM network is applied to predict <span><math><mrow><mi>β</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> obtained by VDWOS, and the prediction solution is highly consistent with the test data. Meanwhile, through sensitivity analysis, the model-based numerical reconstruction solution exhibits significant responsiveness, which neural networks cannot achieve. However, the ODE model and the discrete model exhibit a high degree of consistency in their specific numerical conclusions, while the FDE model yields significantly different results. This study provides valuable insights into the crucial issue of model selection in the fields of infectious disease prediction and early warning, pest control, and tumor treatment.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118163"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329809","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

Nonlinear dynamics of taillight effect in mixed traffic flow driven by competing visual delay and V2X communication 竞争视觉延迟和V2X通信驱动下混合交通流尾灯效应的非线性动力学

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-26 DOI: 10.1016/j.chaos.2026.118152

Shuaiyang Jiao , Liyuan Xue , Yubo Li , Juntong Wu , Aizeng Li

{"title":"Nonlinear dynamics of taillight effect in mixed traffic flow driven by competing visual delay and V2X communication","authors":"Shuaiyang Jiao , Liyuan Xue , Yubo Li , Juntong Wu , Aizeng Li","doi":"10.1016/j.chaos.2026.118152","DOIUrl":"10.1016/j.chaos.2026.118152","url":null,"abstract":"<div><div>This study investigates the impact of the taillight effect on the stability of mixed traffic flow. Constrained by physiological limitations, human drivers inevitably exhibit visual reaction delays when perceiving brake lights. Conversely, connected vehicles leverage V2X communication to receive electronic signals, enabling instantaneous feedback and beyond-visual-range perception. These distinct characteristics create a competitive relationship regarding their contributions to system stability. Thus, this study explicitly defines this competition by employing the connected vehicle penetration rate as a weighting parameter. By incorporating this into a lattice hydrodynamic model, we quantify the unique competitive mechanism between the lag of human visual perception and the instantaneity of V2X communication. Through linear stability analysis, we derive the critical stability criterion and reveal how the penetration rate of connected vehicles offsets the instability caused by human physiological delay. On this basis, we carry out nonlinear analysis using the reductive perturbation method to derive the modified mKdV equation near the critical point and obtain the analytical solution for the kink-antikink soliton. Numerical simulations confirm the theoretical predictions and demonstrate that increasing the penetration rate of connected vehicles significantly modifies the dispersion coefficient of traffic flow. These results substantiate that the competition mechanism under the taillight effect effectively eliminates the hysteresis loop and phantom jam caused by visual delay and enhances the robustness of the traffic system against the physiological limitations of human drivers.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118152"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147330311","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

Asynchronous-delay boundary control of general hyperbolic PDEs with zero transport speeds 一般零传输速度双曲偏微分方程的异步延迟边界控制

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-19 DOI: 10.1016/j.chaos.2026.118065

Wei Sun , Jing Li , Liangyu Xu , Jiale Yi

{"title":"Asynchronous-delay boundary control of general hyperbolic PDEs with zero transport speeds","authors":"Wei Sun , Jing Li , Liangyu Xu , Jiale Yi","doi":"10.1016/j.chaos.2026.118065","DOIUrl":"10.1016/j.chaos.2026.118065","url":null,"abstract":"<div><div>This paper focuses on addressing the challenge of compensating for input delays in a broad class of coupled <span><math><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mi>l</mi><mo>+</mo><mi>m</mi><mo>)</mo></mrow></math></span> systems governed by hyperbolic-type partial differential equations with zero transport velocity. The controller is located at the right boundary of the domain and exhibits different delays. Conventional backstepping design is no longer suitable for asynchronous delay problems. To address the challenges posed by asynchronous delays, we develop a backstepping-based compensator and propose a novel asynchronous-backstepping transformation. The transformation kernels are defined over a square domain and feature a more intricate coupling structure, which presents significant challenges for the analysis of well-posedness. We tackle these problems through the employment of characteristic analysis alongside stepwise approximation techniques. Furthermore, since our stability result is exponential, we further demonstrate that the asynchronous-backstepping transformation guarantees the equivalence of norms between the original system states and the target system states. Finally, a numerical example illustrates the effectiveness of the proposed approach.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118065"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777186","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

Mean dimension explosion of induced homeomorphisms 诱导同胚的平均维数爆炸

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-20 DOI: 10.1016/j.chaos.2026.118087

Gabriel Lacerda , Sergio Romaña

{"title":"Mean dimension explosion of induced homeomorphisms","authors":"Gabriel Lacerda , Sergio Romaña","doi":"10.1016/j.chaos.2026.118087","DOIUrl":"10.1016/j.chaos.2026.118087","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi></math></span> be a compact metric space and <span><math><mrow><mi>T</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></mrow></math></span> a continuous function. The induced hyperspace map <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> acts on the hyperspace <span><math><mrow><mi>K</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> of closed and nonempty subsets of <span><math><mi>X</mi></math></span>, and on the continuum hyperspace <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>⊂</mo><mi>K</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> of connected sets. This work studies the mean dimension explosion phenomenon: when the base system <span><math><mi>T</mi></math></span> has zero topological entropy, but the mean dimension of the induced map <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> is infinite. In particular, this phenomenon occurs for Morse–Smale diffeomorphisms. Furthermore, for a circle homeomorphism <span><math><mi>H</mi></math></span>, the mean dimension explosion does not occur if and only if <span><math><mi>H</mi></math></span> is conjugate to a rotation. For the metric mean dimension, a different result is obtained: we establish sufficient conditions for the induced hyperspace map to have zero or infinite metric mean dimension.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118087"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778117","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

On the continuous dependence of the attractors generated by mixed possibly infinite iterated function systems 混合可能无限迭代函数系统吸引子的连续依赖性

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-21 DOI: 10.1016/j.chaos.2026.118029

Bogdan-Cristian Anghelina , Radu Miculescu , Alexandru Mihail

引用次数: 0

Asymptotically period-doubling and Neimark–Sacker bifurcation controls of discrete fractional predator–prey systems 离散分数型捕食者-食饵系统的渐近倍周期和neimmark - sacker分岔控制

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-23 DOI: 10.1016/j.chaos.2026.118078

Hu-Shuang Hou , Guo-Cheng Wu , René Lozi , Zhi-Wen Mo

引用次数: 0

Tunable coexisting states and frequency signatures of a modified Shinriki circuit 改进的Shinriki电路的可调共存状态和频率特征

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-21 DOI: 10.1016/j.chaos.2026.118117

Yizi Cheng , Fuhong Min , Hanxi Liu , Yi Cao , Yeyin Xu

{"title":"Tunable coexisting states and frequency signatures of a modified Shinriki circuit","authors":"Yizi Cheng , Fuhong Min , Hanxi Liu , Yi Cao , Yeyin Xu","doi":"10.1016/j.chaos.2026.118117","DOIUrl":"10.1016/j.chaos.2026.118117","url":null,"abstract":"<div><div>Nonlinear circuits that exhibit pronounced chaos are valued across many engineering fields. To better exploit them, this paper is concerned with tunable coexisting states in a modified Shinriki circuit, with a particular focus on frequency signatures relevant to characterization and design. First, a simple diode-based nonlinear element is constructed, which shows a polarity-selective asymmetric current–voltage (<span><math><mrow><mi>i</mi><mo>−</mo><mi>v</mi></mrow></math></span>) characteristic with an inserted DC-bias. This modification enriches the dynamical manifestations in the modified Shinriki circuit. Under a certain degree of asymmetry, distinct coexisting states are continuously tuned by adjusting the resistance in the RLC loop. Furthermore, based on the implicit mapping approach for autonomous circuits, harmonics across different orders, associated with cascaded coexisting phenomena, are decomposed. These features are systematically examined in bifurcation diagrams, amplitude spectra, and frequency spectra. Finally, the theoretical results are convincingly corroborated by the printed circuit board (PCB). Overall, this study contributes to the understanding and utilization of complex dynamics in nonlinear circuits.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118117"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778548","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

Multi-characteristic heterogeneous attractors: Construction, assessment, and encryption application 多特征异质吸引子：构建、评估及加密应用

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-25 DOI: 10.1016/j.chaos.2026.118147

Xuenan Peng , Cong Ye , Zihan Zhong , Guangfu Luo , Chenqi Dai , Chunlai Li

{"title":"Multi-characteristic heterogeneous attractors: Construction, assessment, and encryption application","authors":"Xuenan Peng , Cong Ye , Zihan Zhong , Guangfu Luo , Chenqi Dai , Chunlai Li","doi":"10.1016/j.chaos.2026.118147","DOIUrl":"10.1016/j.chaos.2026.118147","url":null,"abstract":"<div><div>Chaotic systems, owing to their pseudo-randomness, are widely applied in diverse areas such as random number generation and information security. However, many existing systems suffer from limited complexity and performance degradation in hardware implementations. To address these challenges, this paper proposes a four-dimensional chaotic system that can generate hyperchaotic and coexisting attractors, which are termed as multi-characteristic attractors. By adjusting the signs and magnitudes of the nonlinear terms, as well as the parameters of the linear terms, the system can produce attractors with diverse phases, amplitudes, and topological structures. Moreover, the incorporation of piecewise-linear controllers enables the merging of these attractors, resulting in the emergence of multi-characteristic heterogeneous attractors. To validate its practical viability, the system is implemented on an FPGA platform, and its hardware-level performance is thoroughly evaluated. Finally, a ‘finding seat’ scrambling-based image encryption algorithm is devised that leverages the proposed system as a pseudo-random number generator, thereby demonstrating its potential for information security applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118147"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279143","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

High-dimensional sample entropy for uncovering rich complex structures in data 高维样本熵用于揭示数据中丰富的复杂结构

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-25 DOI: 10.1016/j.chaos.2026.118076

Wenxin Xia , Fang Wang

{"title":"High-dimensional sample entropy for uncovering rich complex structures in data","authors":"Wenxin Xia , Fang Wang","doi":"10.1016/j.chaos.2026.118076","DOIUrl":"10.1016/j.chaos.2026.118076","url":null,"abstract":"<div><div>With the widespread emergence of high-dimensional data in complex systems and practical applications, existing one-dimensional entropy measures and their two-dimensional extensions exhibit significant limitations in capturing spatial information of high-dimensional data and revealing their complex structures. To address this, we propose high-dimensional sample entropy (HDSE), a novel entropy algorithm designed to systematically quantify the complexity and uncertainty of high-dimensional data while establish a unified dimension-agnostic computational framework. This framework extends entropy analysis to data spaces of arbitrary dimensions, thereby avoiding the structural information distortion caused by data reshaping and dimensionality reduction in traditional methods. The core innovation of HDSE lies in directly constructing template sub-blocks in the raw high-dimensional data space by introducing multi-order phase space reconstruction. These sub-blocks exist as hypercubes in the high-dimensional space, enabling them to precisely capture the spatial distribution characteristics of data within local regions. Experimental results demonstrate that HDSE not only maintains theoretically consistent monotonicity across dimensions in synthetic fractional Brownian motion data but also exhibits superior discriminative sensitivity compared to other methods in tests involving three-dimensional mixed process model, validating its advantages in theoretical rigor and practical efficacy. Furthermore, in the classification of rapeseed varieties using RGB image data, features extracted from HDSE consistently surpass those from two-dimensional methods across multiple evaluation metrics. This result confirms HDSE’s capacity to preserve critical structural information in high-dimensional data, establishing it as a more robust analytical tool for complexity assessment and pattern recognition in complex systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118076"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279150","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

Broadband hyperphase pure-high-even-order dispersion solitons from Mamyshev oscillators 来自马米舍夫振荡器的宽带超相纯高偶阶色散孤子

IF 5.6 1区数学

Chaos Solitons & Fractals Pub Date : 2026-07-01 Epub Date: 2026-02-27 DOI: 10.1016/j.chaos.2026.118155

Yingying Li , Qi Li , Bo Gao , Ge Wu , Honglin Wen , Luyao Zhou , Jiayu Huo , Chunyang Ma , Ying Han , Lie Liu

{"title":"Broadband hyperphase pure-high-even-order dispersion solitons from Mamyshev oscillators","authors":"Yingying Li , Qi Li , Bo Gao , Ge Wu , Honglin Wen , Luyao Zhou , Jiayu Huo , Chunyang Ma , Ying Han , Lie Liu","doi":"10.1016/j.chaos.2026.118155","DOIUrl":"10.1016/j.chaos.2026.118155","url":null,"abstract":"<div><div>Mamyshev oscillator (MO) represents a passively mode-locked fiber laser architecture that exhibits strong tolerance to nonlinear phase shifts through its dual-filter structure. The solitons that can accumulate extremely high nonlinear phase shifts in MO are defined here as hyperphase solitons. Meanwhile, pure-high-even-order dispersion (PHEOD) solitons challenge the traditional understanding of dispersion management beyond the second order through their unique energy-width scaling properties. Previous studies have only preliminarily investigated the basic characteristics of PHEOD solitons in saturable-absorber-based mode-locked fiber lasers. However, the generation mechanism, spectral behavior, and underlying physical nature of hyperphase PHEOD solitons in the MO remain unresolved. In this work, we experimentally achieved the stable generation of hyperphase PHEOD solitons in MO and focused on analyzing their spectral sidebands and broadening characteristics. A theoretical model was constructed to describe the formation and evolution of these spectral features, and its accuracy was verified through experiments and numerical simulations. The research results show that the proposed theoretical model can provide an effective tool for the precise analysis of the spectral characteristics of hyperphase PHEOD solitons, not only helping to deeply understand the physical mechanism of PHEOD solitons in MO, but providing important theoretical support for the performance optimization of ultrafast lasers.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118155"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329811","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