Pub Date : 2026-07-01Epub Date: 2026-02-19DOI: 10.1016/j.chaos.2026.118065
Wei Sun , Jing Li , Liangyu Xu , Jiale Yi
This paper focuses on addressing the challenge of compensating for input delays in a broad class of coupled 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.
{"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}
Pub Date : 2026-07-01Epub Date: 2026-02-20DOI: 10.1016/j.chaos.2026.118087
Gabriel Lacerda , Sergio Romaña
Let be a compact metric space and a continuous function. The induced hyperspace map acts on the hyperspace of closed and nonempty subsets of , and on the continuum hyperspace of connected sets. This work studies the mean dimension explosion phenomenon: when the base system has zero topological entropy, but the mean dimension of the induced map is infinite. In particular, this phenomenon occurs for Morse–Smale diffeomorphisms. Furthermore, for a circle homeomorphism , the mean dimension explosion does not occur if and only if 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.
{"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}
Pub Date : 2026-07-01Epub Date: 2026-02-21DOI: 10.1016/j.chaos.2026.118029
Bogdan-Cristian Anghelina , Radu Miculescu , Alexandru Mihail
In our previous paper (Anghelina et al., 2025), we introduced the concept of a mixed possibly infinite iterated function system (for short mIIFS). Such a system comprises a possibly infinite family of Banach contractions and a possibly infinite family of nonexpansive functions which are Banach contractions, not on the whole space, but only on the orbits of the space’s elements. As a consequence, the associated fractal operator turns out to be weakly Picard. Therefore, to every bounded and closed set corresponds a fixed point of the associated fractal operator. In this paper we prove not only the continuous dependence of the attractors of an mIIFS with respect to the associated sets, but also with respect to the constitutive functions. In addition, we give an evaluation of the distance between the attractors of two mIIFSs corresponding to the set mentioned before.
在我们之前的论文（Anghelina et al., 2025）中，我们引入了混合可能无限迭代函数系统（简称mIIFS）的概念。这样一个系统包含可能无限的巴拿赫收缩族和可能无限的非膨胀函数族，它们是巴拿赫收缩，不是在整个空间上，而只是在空间元素的轨道上。因此，相关的分形算子是弱皮卡德算子。因此，对于每一个有界闭集C，对应相应分形算子的不动点AC。本文不仅证明了mIIFS的吸引子对关联集的连续依赖性，而且证明了其对本构函数的连续依赖性。此外，我们给出了两个miifs的吸引子之间的距离的评价，这些miifs对应于前面提到的集合C。
{"title":"On the continuous dependence of the attractors generated by mixed possibly infinite iterated function systems","authors":"Bogdan-Cristian Anghelina , Radu Miculescu , Alexandru Mihail","doi":"10.1016/j.chaos.2026.118029","DOIUrl":"10.1016/j.chaos.2026.118029","url":null,"abstract":"<div><div>In our previous paper (Anghelina et al., 2025), we introduced the concept of a mixed possibly infinite iterated function system (for short mIIFS). Such a system comprises a possibly infinite family of Banach contractions and a possibly infinite family of nonexpansive functions which are Banach contractions, not on the whole space, but only on the orbits of the space’s elements. As a consequence, the associated fractal operator turns out to be weakly Picard. Therefore, to every bounded and closed set <span><math><mi>C</mi></math></span> corresponds a fixed point <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> of the associated fractal operator. In this paper we prove not only the continuous dependence of the attractors of an mIIFS with respect to the associated sets, but also with respect to the constitutive functions. In addition, we give an evaluation of the distance between the attractors of two mIIFSs corresponding to the set <span><math><mi>C</mi></math></span> mentioned before.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118029"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778115","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 : 2026-07-01Epub Date: 2026-02-23DOI: 10.1016/j.chaos.2026.118078
Hu-Shuang Hou , Guo-Cheng Wu , René Lozi , Zhi-Wen Mo
Fractional calculus is a new dimension to describe the complexity of nonlinear systems, but it also leads to difficulty in bifurcation control. This paper provides analytical conditions for actively controlling bifurcations in discrete fractional predator–prey systems, whereas existing studies primarily rely on numerical observations. A rigorous analytical method is established to control both Neimark–Sacker and period-doubling bifurcations. Through eigenvalue analysis, the conditions for the onset of these bifurcations are first derived. Then, it is shown how hybrid and state-feedback controllers can systematically suppress them. Numerical simulations confirm the effectiveness of the theoretical results, providing a solid analytical foundation for managing complex dynamics in ecological systems. The method can also be used in bifurcation controlling in other fractional discrete-time systems.
{"title":"Asymptotically period-doubling and Neimark–Sacker bifurcation controls of discrete fractional predator–prey systems","authors":"Hu-Shuang Hou , Guo-Cheng Wu , René Lozi , Zhi-Wen Mo","doi":"10.1016/j.chaos.2026.118078","DOIUrl":"10.1016/j.chaos.2026.118078","url":null,"abstract":"<div><div>Fractional calculus is a new dimension to describe the complexity of nonlinear systems, but it also leads to difficulty in bifurcation control. This paper provides analytical conditions for actively controlling bifurcations in discrete fractional predator–prey systems, whereas existing studies primarily rely on numerical observations. A rigorous analytical method is established to control both Neimark–Sacker and period-doubling bifurcations. Through eigenvalue analysis, the conditions for the onset of these bifurcations are first derived. Then, it is shown how hybrid and state-feedback controllers can systematically suppress them. Numerical simulations confirm the effectiveness of the theoretical results, providing a solid analytical foundation for managing complex dynamics in ecological systems. The method can also be used in bifurcation controlling in other fractional discrete-time systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118078"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777676","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 : 2026-07-01Epub Date: 2026-02-21DOI: 10.1016/j.chaos.2026.118117
Yizi Cheng , Fuhong Min , Hanxi Liu , Yi Cao , Yeyin Xu
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 () 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.
{"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}
Pub Date : 2026-07-01Epub Date: 2026-02-25DOI: 10.1016/j.chaos.2026.118147
Xuenan Peng , Cong Ye , Zihan Zhong , Guangfu Luo , Chenqi Dai , Chunlai Li
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.
{"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}
Pub Date : 2026-07-01Epub Date: 2026-02-25DOI: 10.1016/j.chaos.2026.118076
Wenxin Xia , Fang Wang
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.
{"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}
Pub Date : 2026-07-01Epub Date: 2026-02-27DOI: 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
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.
{"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}
Pub Date : 2026-07-01Epub Date: 2026-02-27DOI: 10.1016/j.chaos.2026.118084
Zhile Wang , Xiaoli Yu , Yu Guo , Jianhua Yang , Zijian Qiao
This paper constructs a high-dimensional Lorenz–Stenflo model by introducing perturbation parameters based on the Lorenz–Stenflo chaotic system. The theoretical framework of vibrational resonance is established by incorporating both low-frequency and high-frequency excitation signals into the system, where the high-frequency component enhances the system response to low-frequency signal, and thus enable weak-signal detection. Specifically, the dynamical characteristics of chaotic system are modified such that the response amplitude to the low-frequency signal reaches its extremum by tuning the amplitude or frequency of high-frequency signal. The mapping relationship is derived among the response amplitude gain of low-frequency signal, high-frequency excitation parameters, and system parameters. The non-monotonic variation of this relationship with respect to these parameters indicates the occurrence of vibrational resonance in the system. In addition, the output of vibrational resonance system is susceptible to interference under strong noise conditions. To mitigate this issue, the parameterized variational mode decomposition method is employed for preprocessing, effectively suppressing strong noise. Comparative analysis across different evaluation index demonstrates that fractional multiscale phase permutation entropy is suitable for selecting the optimal modal component. Experimental results show that the proposed vibrational resonance system effectively extracts fault features of rolling bearing, thereby validating and extending the applicability of vibrational resonance theory in signal processing.
{"title":"Research on a novel weak fault detection method based on vibrational resonance in high-dimensional chaotic system, and variational mode decomposition","authors":"Zhile Wang , Xiaoli Yu , Yu Guo , Jianhua Yang , Zijian Qiao","doi":"10.1016/j.chaos.2026.118084","DOIUrl":"10.1016/j.chaos.2026.118084","url":null,"abstract":"<div><div>This paper constructs a high-dimensional Lorenz–Stenflo model by introducing perturbation parameters based on the Lorenz–Stenflo chaotic system. The theoretical framework of vibrational resonance is established by incorporating both low-frequency and high-frequency excitation signals into the system, where the high-frequency component enhances the system response to low-frequency signal, and thus enable weak-signal detection. Specifically, the dynamical characteristics of chaotic system are modified such that the response amplitude to the low-frequency signal reaches its extremum by tuning the amplitude or frequency of high-frequency signal. The mapping relationship is derived among the response amplitude gain of low-frequency signal, high-frequency excitation parameters, and system parameters. The non-monotonic variation of this relationship with respect to these parameters indicates the occurrence of vibrational resonance in the system. In addition, the output of vibrational resonance system is susceptible to interference under strong noise conditions. To mitigate this issue, the parameterized variational mode decomposition method is employed for preprocessing, effectively suppressing strong noise. Comparative analysis across different evaluation index demonstrates that fractional multiscale phase permutation entropy is suitable for selecting the optimal modal component. Experimental results show that the proposed vibrational resonance system effectively extracts fault features of rolling bearing, thereby validating and extending the applicability of vibrational resonance theory in signal processing.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118084"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329814","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 : 2026-07-01Epub Date: 2026-02-21DOI: 10.1016/j.chaos.2026.118081
Yago Emanoel Ramos , Raphael Silva do Rosário , Adriana de Faria Gehres , Maria João Alves , Ana Maria Leitão , Cecília Bastos da Costa Accioly , Fatima Wachowicz , Ivani Lúcia Oliveira de Santana , José Garcia Vivas Miranda
Collective improvisation in dance provides a rich natural laboratory for investigating emergent coordination in coupled neuro-motor systems. Here, we examine how training shapes spontaneous synchronization patterns across movement dynamics and brain activity during collaborative performance, with particular emphasis on the structure of higher-order interactions. Using a dual-recording protocol integrating 3D motion capture and hyperscanning EEG, participants engaged in free, interaction-driven, and rule-based improvisation tasks before and after a generative dance program grounded in cellular automata principles. Motor behavior was characterized through a time-resolved α-exponent derived from Movement Element Decomposition, capturing fluctuations in energetic strategies and the exploration of degrees of freedom. Synchronization events were quantified using Motif Synchronization for biomechanical data and multilayer Time-Varying Graphs for neural data. In order to investigate collective organization beyond pairwise coupling, biomechanical synchronization networks were further analyzed using simplicial complexes, allowing the characterization of interaction structures at multiple orders, including dyads, triads, and quartets. The results reveal that training modulates the distribution of interaction orders, with pronounced effects at the pairwise level. In parallel, neural data indicate increased inter-brain synchronization following training, particularly in frontal regions, suggesting enhanced alignment of internal cognitive and intentional processes. Together, these findings suggest that togetherness in collaborative improvisation emerges as a high-order dynamical property of social systems rather than as mere motor similarity. This study highlights the nonlinear and hierarchical nature of social coordination and offers a principled framework for modeling collective behavior in creative human systems.
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