Pub Date : 2026-01-14DOI: 10.1016/j.chaos.2026.117914
Zbigniew Czechowski , Luciano Telesca
Asymmetry in persistence introduces an additional directed force that alters the dynamics of stochastic processes, potentially affecting the behavior of extremes in their realizations (time series). In this work, we investigate these effect, unexplored so far, using a modified Langevin model that incorporates an asymmetric persistence mechanism. Extremes are defined through run theory and analyzed using informational measures, alongside examining the topological properties of visibility graphs constructed from the point processes of extremes. Our results reveal a systematic influence of asymmetry on the behavior of extremes—both their size and magnitude decrease with increasing asymmetry, while their degree of order, quantified by Shannon entropy, increases.
{"title":"Effect of asymmetric persistence in the modified nonlinear Langevin model on behavior of extremes in generated time series","authors":"Zbigniew Czechowski , Luciano Telesca","doi":"10.1016/j.chaos.2026.117914","DOIUrl":"10.1016/j.chaos.2026.117914","url":null,"abstract":"<div><div>Asymmetry in persistence introduces an additional directed force that alters the dynamics of stochastic processes, potentially affecting the behavior of extremes in their realizations (time series). In this work, we investigate these effect, unexplored so far, using a modified Langevin model that incorporates an asymmetric persistence mechanism. Extremes are defined through run theory and analyzed using informational measures, alongside examining the topological properties of visibility graphs constructed from the point processes of extremes. Our results reveal a systematic influence of asymmetry on the behavior of extremes—both their size and magnitude decrease with increasing asymmetry, while their degree of order, quantified by Shannon entropy, increases.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117914"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976352","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117902
Xuyang Wang , Xin Ning , Zheng Wang , Zhansheng Chen
This paper proposes a fixed-time stability-based control strategy for high-speed unmanned systems (HSUSs) considering practical switching topology scenarios. First, a fixed-time disturbance observer (FixTDO) with initial condition-independent convergence time is designed to handle the system disturbances. Subsequently, an auxiliary system is constructed to address communication switching topology constraints. Furthermore, a fixed-time controller is synthesized to enhance transient performance and system robustness, with a first-order filter incorporated to eliminate differentiation-induced computational divergence. Finally, comparative simulation studies validate the effectiveness and operational feasibility of the proposed algorithm.
{"title":"Fixed-time control strategy for high-speed unmanned system under switching topology","authors":"Xuyang Wang , Xin Ning , Zheng Wang , Zhansheng Chen","doi":"10.1016/j.chaos.2026.117902","DOIUrl":"10.1016/j.chaos.2026.117902","url":null,"abstract":"<div><div>This paper proposes a fixed-time stability-based control strategy for high-speed unmanned systems (HSUSs) considering practical switching topology scenarios. First, a fixed-time disturbance observer (FixTDO) with initial condition-independent convergence time is designed to handle the system disturbances. Subsequently, an auxiliary system is constructed to address communication switching topology constraints. Furthermore, a fixed-time controller is synthesized to enhance transient performance and system robustness, with a first-order filter incorporated to eliminate differentiation-induced computational divergence. Finally, comparative simulation studies validate the effectiveness and operational feasibility of the proposed algorithm.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117902"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976411","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117893
Lifen Yan, Mingfeng Wang, Dong Zhang, Haiyong Zhu
We predict the existence of petal-like vortex solitons (PVSs) carrying fractional angular momentum in a defocusing cubic nonlinear medium modulated by the cylindrical Bessel optical lattice. Linear stability analysis and direct simulations show that PVSs remain stable when the propagation constant exceeds a critical value but revert to a ring vortex soliton at a second threshold. Fundamental fractional vortex soliton possesses an opening gap in the intensity ring, and its power and angular momentum per photon vary continuously with the propagating constant. Higher-order PVS exhibits an odd number of petals, which results from a complex phase distribution containing an equal number of phase dislocations. Specifically, the stability domain of the soliton shrinks as the number of petals increases.
{"title":"Petal-like vortex solitons with fractional angular momentum in Bessel optical lattices","authors":"Lifen Yan, Mingfeng Wang, Dong Zhang, Haiyong Zhu","doi":"10.1016/j.chaos.2026.117893","DOIUrl":"10.1016/j.chaos.2026.117893","url":null,"abstract":"<div><div>We predict the existence of petal-like vortex solitons (PVSs) carrying fractional angular momentum in a defocusing cubic nonlinear medium modulated by the cylindrical Bessel optical lattice. Linear stability analysis and direct simulations show that PVSs remain stable when the propagation constant exceeds a critical value but revert to a ring vortex soliton at a second threshold. Fundamental fractional vortex soliton possesses an opening gap in the intensity ring, and its power and angular momentum per photon vary continuously with the propagating constant. Higher-order PVS exhibits an odd number of petals, which results from a complex phase distribution containing an equal number of phase dislocations. Specifically, the stability domain of the soliton shrinks as the number of petals increases.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117893"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962059","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117877
Yifeng Zhang , Wei Zhang , Yufei Zhang
Low-altitude aircrafts are subject to complex aerodynamic and environmental disturbances, which place stringent demands on lightweight structures with reliable dynamic stability. Functionally graded graphene-reinforced composites (FG-GRCs), owing to their high specific strength and tunable properties, are promising candidates for load-bearing and vibration-sensitive components in such vehicles. This study investigates the complex nonlinear dynamics, particularly multi-pulse chaotic vibrations, of cantilever laminated curved plate subjected simultaneous transverse and in-plane parametric excitations. A nonlinear dynamic model incorporating geometric curvature and material gradation effects is established and validated by finite element analysis, revealing a critical 1:1 internal resonance between specific modes under particular geometric configurations. The extended Melnikov method is applied to theoretically predict the Shilnikov-type multi-pulse chaotic motions. Bi-parameter threshold surfaces derived from the Melnikov function are proposed and quantitatively validated against two-dimensional maximum Lyapunov exponent (MLE) diagrams, exhibiting good agreement in identifying chaotic regions. Extensive numerical simulations, including bifurcation diagrams, phase portraits, Poincaré maps, and time histories, confirm the presence of complex dynamics such as periodic motions, chaotic vibrations, and their transitions. The results provide crucial insights into the parameter domains that may trigger hazardous chaotic responses in FG-GRC curved plates, supporting the safe and reliable design of next-generation low-altitude aircraft structures such as wings, rotor arms, and fuselage skins.
{"title":"Nonlinear chaotic dynamics of functionally graded graphene composite curved plates for the wings of low-altitude aircrafts","authors":"Yifeng Zhang , Wei Zhang , Yufei Zhang","doi":"10.1016/j.chaos.2026.117877","DOIUrl":"10.1016/j.chaos.2026.117877","url":null,"abstract":"<div><div>Low-altitude aircrafts are subject to complex aerodynamic and environmental disturbances, which place stringent demands on lightweight structures with reliable dynamic stability. Functionally graded graphene-reinforced composites (FG-GRCs), owing to their high specific strength and tunable properties, are promising candidates for load-bearing and vibration-sensitive components in such vehicles. This study investigates the complex nonlinear dynamics, particularly multi-pulse chaotic vibrations, of cantilever laminated curved plate subjected simultaneous transverse and in-plane parametric excitations. A nonlinear dynamic model incorporating geometric curvature and material gradation effects is established and validated by finite element analysis, revealing a critical 1:1 internal resonance between specific modes under particular geometric configurations. The extended Melnikov method is applied to theoretically predict the Shilnikov-type multi-pulse chaotic motions. Bi-parameter threshold surfaces derived from the Melnikov function are proposed and quantitatively validated against two-dimensional maximum Lyapunov exponent (MLE) diagrams, exhibiting good agreement in identifying chaotic regions. Extensive numerical simulations, including bifurcation diagrams, phase portraits, Poincaré maps, and time histories, confirm the presence of complex dynamics such as periodic motions, chaotic vibrations, and their transitions. The results provide crucial insights into the parameter domains that may trigger hazardous chaotic responses in FG-GRC curved plates, supporting the safe and reliable design of next-generation low-altitude aircraft structures such as wings, rotor arms, and fuselage skins.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117877"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976349","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117907
Yijie Huang
Integrating reputation mechanisms with dynamic networks effectively facilitates collective cooperation in complex networks. However, existing studies only adjust network structures directly via reputation, ignoring the driving role of individual payoffs in network evolution. To address this gap, this paper proposes a reputation-payoff-network synergetic evolution framework and explores how reputation-dependent, payoff-driven dynamic networks promote cooperative behaviors. Results show that this synergetic evolution model significantly enhances collective cooperation, with its effectiveness depending on both the magnitude of the temptation to defect and the value of the reputation sensitivity factor. Specifically, when the temptation is small, the cooperation rate remains generally high, and the reputation sensitivity factor has no significant impact. In contrast, when the temptation is large, a high cooperation rate can be stably maintained only if the reputation sensitivity factor is small. This study confirms that regulating payoffs through reputation and subsequently allowing payoffs to drive the dynamic adjustment of network connections enables the establishment of an efficient cooperation-facilitating mechanism. Consequently, it provides new insights and theoretical support for guiding cooperative behaviors in complex networks.
{"title":"Evolution of cooperation on a dynamic network driven by reputation-dependent payoffs","authors":"Yijie Huang","doi":"10.1016/j.chaos.2026.117907","DOIUrl":"10.1016/j.chaos.2026.117907","url":null,"abstract":"<div><div>Integrating reputation mechanisms with dynamic networks effectively facilitates collective cooperation in complex networks. However, existing studies only adjust network structures directly via reputation, ignoring the driving role of individual payoffs in network evolution. To address this gap, this paper proposes a reputation-payoff-network synergetic evolution framework and explores how reputation-dependent, payoff-driven dynamic networks promote cooperative behaviors. Results show that this synergetic evolution model significantly enhances collective cooperation, with its effectiveness depending on both the magnitude of the temptation to defect and the value of the reputation sensitivity factor. Specifically, when the temptation is small, the cooperation rate remains generally high, and the reputation sensitivity factor has no significant impact. In contrast, when the temptation is large, a high cooperation rate can be stably maintained only if the reputation sensitivity factor is small. This study confirms that regulating payoffs through reputation and subsequently allowing payoffs to drive the dynamic adjustment of network connections enables the establishment of an efficient cooperation-facilitating mechanism. Consequently, it provides new insights and theoretical support for guiding cooperative behaviors in complex networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117907"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976410","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117916
Yuke Tang, Xiaosheng Feng, Tingkai Zhao, Baoxiang Du
To address the challenges of expensive hardware implementation for high-dimensional continuous Hopfield neural networks(HNNs) and the limited dynamic phenomena observed in low-dimensional discrete HNNs, this system combines low-dimensional architecture and rich dynamic characteristics, and realizes the control of arbitrary direction and quantity of multi-fold attractors under memristor domination. The memristor internally incorporates an odd-even quantity controller for attractors. Through adjustment via this controller, it can precisely achieve the regulation of multi-fold attractors with arbitrary quantities and directions within 1-3 dimensional spaces. An in-depth analysis was conducted on the impacts of memristive coupling strength, internal scale factors, and initial values on dynamics, leading to the discovery of implicit dynamics such as spatial initial offset and symmetric separation and expansion. Through bifurcation diagrams, Lyapunov exponents, and complexity analysis, the system’s complex chaotic behavior was verified from multiple perspectives. The model’s feasibility was validated via Digital signal processor (DSP) hardware implementation. A pseudo random number generator (PRNG) designed based on its output passed NIST testing, demonstrating strong randomness.
{"title":"Design of spatially multi-structure attractors in discrete memristive Hopfield neural networks","authors":"Yuke Tang, Xiaosheng Feng, Tingkai Zhao, Baoxiang Du","doi":"10.1016/j.chaos.2026.117916","DOIUrl":"10.1016/j.chaos.2026.117916","url":null,"abstract":"<div><div>To address the challenges of expensive hardware implementation for high-dimensional continuous Hopfield neural networks(HNNs) and the limited dynamic phenomena observed in low-dimensional discrete HNNs, this system combines low-dimensional architecture and rich dynamic characteristics, and realizes the control of arbitrary direction and quantity of multi-fold attractors under memristor domination. The memristor internally incorporates an odd-even quantity controller for attractors. Through adjustment via this controller, it can precisely achieve the regulation of multi-fold attractors with arbitrary quantities and directions within 1-3 dimensional spaces. An in-depth analysis was conducted on the impacts of memristive coupling strength, internal scale factors, and initial values on dynamics, leading to the discovery of implicit dynamics such as spatial initial offset and symmetric separation and expansion. Through bifurcation diagrams, Lyapunov exponents, and complexity analysis, the system’s complex chaotic behavior was verified from multiple perspectives. The model’s feasibility was validated via Digital signal processor (DSP) hardware implementation. A pseudo random number generator (PRNG) designed based on its output passed NIST testing, demonstrating strong randomness.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117916"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976371","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117864
Junchao Zou, Ronghao Wang, Jun Yan, Kefeng Huang, Zhenrong Yuan
This paper presents an effective method for analyzing and optimizing the stability of a three-phase rectifier system cascaded with DC-DC converters under generalized PI control. The study focuses on non-smooth chaotic phenomena caused by boundary collision bifurcation. Through stroboscopic mapping and Floquet theory, the method analyzes bifurcation behavior with respect to both control and circuit parameters, accurately identifying feasible parameter regions with clear stability boundaries. This bifurcation-based approach provides clearer insights into chaotic mechanisms and requires less computational effort compared to conventional methods. To achieve optimal performance within this complex parameter space, a Chaotic Evolution Optimization (CEO) algorithm is developed. The algorithm efficiently explores high-dimensional parameter spaces using chaotic dynamics, suppresses PWM saturation, and improves stability by systematically minimizing a composite objective function. This transforms heuristic parameter tuning into a stability-constrained optimization process. The resulting methodology reduces dependence on empirical experience while enhancing resilience to load variations, enabling more reliable system operation across different working conditions.
{"title":"Chaos evolution optimization with feasible region analysis for stability enhancement in cascaded converters","authors":"Junchao Zou, Ronghao Wang, Jun Yan, Kefeng Huang, Zhenrong Yuan","doi":"10.1016/j.chaos.2026.117864","DOIUrl":"10.1016/j.chaos.2026.117864","url":null,"abstract":"<div><div>This paper presents an effective method for analyzing and optimizing the stability of a three-phase rectifier system cascaded with DC-DC converters under generalized PI control. The study focuses on non-smooth chaotic phenomena caused by boundary collision bifurcation. Through stroboscopic mapping and Floquet theory, the method analyzes bifurcation behavior with respect to both control and circuit parameters, accurately identifying feasible parameter regions with clear stability boundaries. This bifurcation-based approach provides clearer insights into chaotic mechanisms and requires less computational effort compared to conventional methods. To achieve optimal performance within this complex parameter space, a Chaotic Evolution Optimization (CEO) algorithm is developed. The algorithm efficiently explores high-dimensional parameter spaces using chaotic dynamics, suppresses PWM saturation, and improves stability by systematically minimizing a composite objective function. This transforms heuristic parameter tuning into a stability-constrained optimization process. The resulting methodology reduces dependence on empirical experience while enhancing resilience to load variations, enabling more reliable system operation across different working conditions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117864"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976372","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 : 2026-01-14DOI: 10.1016/j.chaos.2026.117899
Jiale Zhang , Jiaquan Xie , Wei Shi
To address the coexistence of steady-state responses in the viscoelastic column subjected to multifrequency excitation, this study for the first time introduces the generalized fractional-order constitutive model into the dynamic modeling of viscoelastic columns subjected to multi-frequency excitation, and establishes the governing equation that is more consistent with the actual mechanical behavior of materials. By performing dimensional reduction through the single mode approximation and the Galerkin method, and subsequently applying the method of multiple scales, the steady-state solutions of the system are derived. The existence conditions of these steady-states are then determined by the Routh-Hurwitz criterion. Through analyses of steady-state response curves, basins of attraction, time series, and phase diagram, a novel multi-stability phenomenon characterized by the long-term coexistence of four stable periodic attractors in the system is revealed. Furthermore, combining the weighted truncated Shannon entropy based on Wada index and the grid method, the partial Wada basin boundaries are quantitatively characterized. The modulation effects of damping and external forcing amplitude on the multistable structures are also examined. Overall, the results break through the limitations of traditional integer-order constitutive relations in the dynamic analysis of viscoelastic materials, and provide theoretical insight for the dynamical analysis of fractional-order viscoelastic columns and offer guidance for engineering vibration control.
{"title":"Multistable responses and Wada basin boundaries in the fractional-order viscoelastic column","authors":"Jiale Zhang , Jiaquan Xie , Wei Shi","doi":"10.1016/j.chaos.2026.117899","DOIUrl":"10.1016/j.chaos.2026.117899","url":null,"abstract":"<div><div>To address the coexistence of steady-state responses in the viscoelastic column subjected to multifrequency excitation, this study for the first time introduces the generalized fractional-order constitutive model into the dynamic modeling of viscoelastic columns subjected to multi-frequency excitation, and establishes the governing equation that is more consistent with the actual mechanical behavior of materials. By performing dimensional reduction through the single mode approximation and the Galerkin method, and subsequently applying the method of multiple scales, the steady-state solutions of the system are derived. The existence conditions of these steady-states are then determined by the Routh-Hurwitz criterion. Through analyses of steady-state response curves, basins of attraction, time series, and phase diagram, a novel multi-stability phenomenon characterized by the long-term coexistence of four stable periodic attractors in the system is revealed. Furthermore, combining the weighted truncated Shannon entropy based on Wada index and the grid method, the partial Wada basin boundaries are quantitatively characterized. The modulation effects of damping and external forcing amplitude on the multistable structures are also examined. Overall, the results break through the limitations of traditional integer-order constitutive relations in the dynamic analysis of viscoelastic materials, and provide theoretical insight for the dynamical analysis of fractional-order viscoelastic columns and offer guidance for engineering vibration control.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117899"},"PeriodicalIF":5.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976348","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 : 2026-01-13DOI: 10.1016/j.chaos.2026.117874
Ivan D. Kolesnikov, Nadezhda Semenova
Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming a neural network into a tangible device. In terms of hardware neural networks, it is more important to consider not only the effect of noise on the input signal, but also the effect of internal noise coming from various network components. In this paper, we investigate how internal noise affects the final performance of feedforward neural networks (FNN) and echo state networks (ESN) during the training of neural networks. The types of noise considered in this paper were originally inspired by a real optical implementation of a neural network. However, these types were subsequently generalized to enhance the applicability of our findings on a broader scale. The noise types considered include additive and multiplicative noise, which depend on how noise influences each individual neuron, and common and uncommon noise, which pertains to the impact of noise on groups of neurons (such as the hidden layer of FNNs or the reservoir of ESNs). In this paper, we demonstrate that, in most cases, both deep and echo state networks benefit from internal noise during training, as it enhances their resilience to noise. Consequently, the testing performance at the same noise intensities is significantly higher for networks trained with noise than for those trained without it. Only multiplicative common noise during training has almost no impact on both deep and recurrent networks.
{"title":"Internal noise in analog neural networks helps with learning","authors":"Ivan D. Kolesnikov, Nadezhda Semenova","doi":"10.1016/j.chaos.2026.117874","DOIUrl":"10.1016/j.chaos.2026.117874","url":null,"abstract":"<div><div>Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming a neural network into a tangible device. In terms of hardware neural networks, it is more important to consider not only the effect of noise on the input signal, but also the effect of internal noise coming from various network components. In this paper, we investigate how internal noise affects the final performance of feedforward neural networks (FNN) and echo state networks (ESN) during the training of neural networks. The types of noise considered in this paper were originally inspired by a real optical implementation of a neural network. However, these types were subsequently generalized to enhance the applicability of our findings on a broader scale. The noise types considered include additive and multiplicative noise, which depend on how noise influences each individual neuron, and common and uncommon noise, which pertains to the impact of noise on groups of neurons (such as the hidden layer of FNNs or the reservoir of ESNs). In this paper, we demonstrate that, in most cases, both deep and echo state networks benefit from internal noise during training, as it enhances their resilience to noise. Consequently, the testing performance at the same noise intensities is significantly higher for networks trained with noise than for those trained without it. Only multiplicative common noise during training has almost no impact on both deep and recurrent networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117874"},"PeriodicalIF":5.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950160","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 : 2026-01-13DOI: 10.1016/j.chaos.2026.117888
Xinlu Yang, Wenbo Wang
Low-frequency oscillation (LFO) identification in wide-area power systems is often hindered by strong noise interference and inaccurate estimation of oscillatory modes. To address these challenges, this paper proposes a novel method that integrates a fractal-ridge-optimized multi-synchrosqueezing transform (MSST) with a fitting-error-minimized matrix pencil (MP). Specifically, a fractal dimension strategy based on box-counting analysis adaptively selects the number of reconstruction ridges, enabling reliable separation of signal and noise components. In addition, a quadratic correction algorithm refines ridge trajectories to suppress spectral distortions and improve time–frequency concentration. Finally, the MP algorithm is enhanced with a fitting-error minimization criterion for adaptive order determination, preventing spurious modes and ensuring accurate parameter estimation. Experimental results show that, for input SNR = 10 dB, the proposed approach improves output SNR by 10.08 dB, while the average estimation errors are as low as 0.001 for frequency and damping, and about 0.008 for amplitude and phase. These findings demonstrate that the proposed method substantially improves noise resistance and parameter accuracy, providing a reliable tool for practical LFO monitoring in wide-area power systems.
{"title":"Low-frequency oscillation identification through fractal-ridge-optimized MSST and fitting-error-minimized MP","authors":"Xinlu Yang, Wenbo Wang","doi":"10.1016/j.chaos.2026.117888","DOIUrl":"10.1016/j.chaos.2026.117888","url":null,"abstract":"<div><div>Low-frequency oscillation (LFO) identification in wide-area power systems is often hindered by strong noise interference and inaccurate estimation of oscillatory modes. To address these challenges, this paper proposes a novel method that integrates a fractal-ridge-optimized multi-synchrosqueezing transform (MSST) with a fitting-error-minimized matrix pencil (MP). Specifically, a fractal dimension strategy based on box-counting analysis adaptively selects the number of reconstruction ridges, enabling reliable separation of signal and noise components. In addition, a quadratic correction algorithm refines ridge trajectories to suppress spectral distortions and improve time–frequency concentration. Finally, the MP algorithm is enhanced with a fitting-error minimization criterion for adaptive order determination, preventing spurious modes and ensuring accurate parameter estimation. Experimental results show that, for input SNR = 10 dB, the proposed approach improves output SNR by 10.08 dB, while the average estimation errors are as low as 0.001 for frequency and damping, and about 0.008 for amplitude and phase. These findings demonstrate that the proposed method substantially improves noise resistance and parameter accuracy, providing a reliable tool for practical LFO monitoring in wide-area power systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117888"},"PeriodicalIF":5.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950163","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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