Pub Date : 2025-01-21DOI: 10.1016/j.chaos.2025.116036
Xiaoqing Ma, Grzegorz Litak, Shengxi Zhou
Nonlinear wind-induced vibration energy harvesters have rich response dynamic behaviors, and diagnosing these response characteristics is crucial for promoting their application. This paper uses the analysis method of “0–1 test” to distinguish response characteristics of bistable and tristable vortex-induced vibration energy harvesters (VIVEHs), and the identification results are compared with the phase portraits, frequency spectrum and Lyapunov exponents. Results indicate that the analysis method of “0–1 test” can effectively distinguish the periodic and chaotic behaviors of the nonlinear VIVEHs by the trajectories of p-q, asymptotic growth rate K(c) and the mean square displacement Mc(n). Overall, this study indicates that the “0–1 test” method is feasible and reliable for identifying the dynamic characteristics of nonlinear vibration energy harvesters, which is meaningful to the optimization analysis of such harvesters.
{"title":"Using 0–1 test to diagnose periodic and chaotic motions of nonlinear vortex-induced vibration energy harvesters","authors":"Xiaoqing Ma, Grzegorz Litak, Shengxi Zhou","doi":"10.1016/j.chaos.2025.116036","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116036","url":null,"abstract":"Nonlinear wind-induced vibration energy harvesters have rich response dynamic behaviors, and diagnosing these response characteristics is crucial for promoting their application. This paper uses the analysis method of “0–1 test” to distinguish response characteristics of bistable and tristable vortex-induced vibration energy harvesters (VIVEHs), and the identification results are compared with the phase portraits, frequency spectrum and Lyapunov exponents. Results indicate that the analysis method of “0–1 test” can effectively distinguish the periodic and chaotic behaviors of the nonlinear VIVEHs by the trajectories of <ce:italic>p</ce:italic>-<ce:italic>q</ce:italic>, asymptotic growth rate <ce:italic>K</ce:italic>(<ce:italic>c</ce:italic>) and the mean square displacement <ce:italic>M</ce:italic><ce:inf loc=\"post\"><ce:italic>c</ce:italic></ce:inf>(<ce:italic>n</ce:italic>). Overall, this study indicates that the “0–1 test” method is feasible and reliable for identifying the dynamic characteristics of nonlinear vibration energy harvesters, which is meaningful to the optimization analysis of such harvesters.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"112 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-20DOI: 10.1016/j.chaos.2025.116021
Muhammad Nadeem, Admilson T. Franco, Imran Siddique, Yamid J. Garcia-Blanco, Luis H. Quitian-Ardila, Rizwan Khan
This study examines the complex interactions between several parameters, such as electro-osmosis force, activation energy, and Darcy-Forchheimer Law, in the magnetohydrodynamic (MHD) Williamson AA7072+AA7075/SA hybrid nanofluid flow over a moving thin needle as alloy nanoparticles AA7075 and AA7072 are inserted into host fluid, sodium alginate (SA). Further, the significance of viscous dissipation, nonlinear thermal radiation, heat absorption/generation, and thermal and concentration convective boundary conditions have been considered to optimize heat and mass transmission. Our approach involves formulating mathematical equations that are then converted into a group of partial differential equations to simulate these intricate processes. These equations become ordinary differential equations through a similarity renovation, and we solve the resulting boundary value problem numerically, implementing the fourth-order accurate BVP4C method. An analysis has been conducted using graphics and tabular to show how many critical physical flow parameters, including temperature ratio, nanoparticle volume fraction, Weissenberg number, magnetic field, and electro-osmotic parameters, affect the mass transfer rate, drag force, flow rate, heat transfer rate, heat, and mass fluxes. The BVP4C solution exhibits absolute compatibility with the artificial neural network (ANN) solution when the numerical solutions are compared to ANN. Fluid temperature rises in response to electro-osmotic parameters, viscoelastic parameters, magnetic field, and nanoparticle volume percentage, but fluid velocity drops, according to the study's prior observations. Moreover, as the activation energy and volume percentage of nanoparticles change, the fluid concentration increases. Drag force and heat transfer rate diminish with increasing electro-osmotic impact.
{"title":"Role of electroosmotic and Darcy-Forchheimer Law on magnetohydrodynamic Williamson hybrid nanofluid flow over a moving thin needle","authors":"Muhammad Nadeem, Admilson T. Franco, Imran Siddique, Yamid J. Garcia-Blanco, Luis H. Quitian-Ardila, Rizwan Khan","doi":"10.1016/j.chaos.2025.116021","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116021","url":null,"abstract":"This study examines the complex interactions between several parameters, such as electro-osmosis force, activation energy, and Darcy-Forchheimer Law, in the magnetohydrodynamic (MHD) Williamson <mml:math altimg=\"si57.svg\"><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>AA</mml:mi><mml:mn>7072</mml:mn><mml:mo>+</mml:mo><mml:mi>AA</mml:mi><mml:mn>7075</mml:mn><mml:mo>/</mml:mo><mml:mi>SA</mml:mi></mml:mrow></mml:mfenced></mml:math> hybrid nanofluid flow over a moving thin needle as alloy nanoparticles AA7075 and AA7072 are inserted into host fluid, sodium alginate (SA). Further, the significance of viscous dissipation, nonlinear thermal radiation, heat absorption/generation, and thermal and concentration convective boundary conditions have been considered to optimize heat and mass transmission. Our approach involves formulating mathematical equations that are then converted into a group of partial differential equations to simulate these intricate processes. These equations become ordinary differential equations through a similarity renovation, and we solve the resulting boundary value problem numerically, implementing the fourth-order accurate BVP4C method. An analysis has been conducted using graphics and tabular to show how many critical physical flow parameters, including temperature ratio, nanoparticle volume fraction, Weissenberg number, magnetic field, and electro-osmotic parameters, affect the mass transfer rate, drag force, flow rate, heat transfer rate, heat, and mass fluxes. The BVP4C solution exhibits absolute compatibility with the artificial neural network (ANN) solution when the numerical solutions are compared to ANN. Fluid temperature rises in response to electro-osmotic parameters, viscoelastic parameters, magnetic field, and nanoparticle volume percentage, but fluid velocity drops, according to the study's prior observations. Moreover, as the activation energy and volume percentage of nanoparticles change, the fluid concentration increases. Drag force and heat transfer rate diminish with increasing electro-osmotic impact.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"57 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-20DOI: 10.1016/j.chaos.2025.116026
Xinzong Wang, Xiaofang Kang, Ling Ji, Ao Zhang, Guanghui Xia
The bionic structure has unique nonlinear properties that can effectively broaden the energy harvesting band. Currently, this energy harvesting device lacks adjustability and adaptability to different environments. Inspired by the tracheas of the lungs, a lung trachea bio-inspired structure (LTBS) is proposed. The main structure of LTBS consists of springs, rods, gears and piezoelectric elements. The novelty of this model is the ability to adapt to different excitation environments by adjusting the steady-state model through rotating gears. The energy harvesting of the system is investigated using the RMS value of the induced voltage and the energy harvesting advantages and disadvantages characteristics are compared at various steady states. The coexisting basins of attraction are mapped and the best optimization scheme to improve its energy harvesting performance is obtained. An impulse perturbation was subsequently initiated to test the model. The test results show that the tri-stable to hexa-stable states exhibit excellent energy harvesting performance in low frequency and low amplitude excitation environments. The initiation of impulse perturbations significantly alters the energy harvesting efficiency and kinematic properties of the system and is limited by the basins of attraction of the system.
{"title":"Low frequency vibration energy harvesting of bio-inspired multi-stable piezoelectric vibration system with an adjustable device","authors":"Xinzong Wang, Xiaofang Kang, Ling Ji, Ao Zhang, Guanghui Xia","doi":"10.1016/j.chaos.2025.116026","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116026","url":null,"abstract":"The bionic structure has unique nonlinear properties that can effectively broaden the energy harvesting band. Currently, this energy harvesting device lacks adjustability and adaptability to different environments. Inspired by the tracheas of the lungs, a lung trachea bio-inspired structure (LTBS) is proposed. The main structure of LTBS consists of springs, rods, gears and piezoelectric elements. The novelty of this model is the ability to adapt to different excitation environments by adjusting the steady-state model through rotating gears. The energy harvesting of the system is investigated using the RMS value of the induced voltage and the energy harvesting advantages and disadvantages characteristics are compared at various steady states. The coexisting basins of attraction are mapped and the best optimization scheme to improve its energy harvesting performance is obtained. An impulse perturbation was subsequently initiated to test the model. The test results show that the tri-stable to hexa-stable states exhibit excellent energy harvesting performance in low frequency and low amplitude excitation environments. The initiation of impulse perturbations significantly alters the energy harvesting efficiency and kinematic properties of the system and is limited by the basins of attraction of the system.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"240 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-20DOI: 10.1016/j.chaos.2025.116004
Yuhao Zhou, Faming Gong, Yanwei Wang, Ruijie Wang, An Zeng
The rapid proliferation of scientific and technological works has highlighted the necessity to effectively identify the significant achievements in more and more complex citation networks. Mainstream algorithms fall into two categories: structural information based algorithms with Citation and PageRank as the core; Temporal information based algorithms represented by the citation dynamic model and Relevance. This article conducts a detailed study of the relationship between these two categories to fill the gap in this area. We use the American Physical Society (APS) dataset, which includes 469,452 papers and 5,016,382 citations from 1893 to 2010. Our findings indicate that PageRank and Citation are statistically similar, both favoring older articles. However, Relevance excels in early forecasting, hence showing a weaker correlation with PageRank. Inspired by this, we introduce a new method called Structural-Temporal Rank (STRank). Validation experiments demonstrate that STRank excels in identifying milestone letters and predicting future impact, outperforming other methods in these tasks. This study introduces the idea of fusing structural and temporal information in designing ranking methods that could guide the future development of more efficient node identification algorithms in networks.
{"title":"Fusing structural and temporal information in citation networks for identifying milestone works","authors":"Yuhao Zhou, Faming Gong, Yanwei Wang, Ruijie Wang, An Zeng","doi":"10.1016/j.chaos.2025.116004","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116004","url":null,"abstract":"The rapid proliferation of scientific and technological works has highlighted the necessity to effectively identify the significant achievements in more and more complex citation networks. Mainstream algorithms fall into two categories: structural information based algorithms with Citation and PageRank as the core; Temporal information based algorithms represented by the citation dynamic model and Relevance. This article conducts a detailed study of the relationship between these two categories to fill the gap in this area. We use the American Physical Society (APS) dataset, which includes 469,452 papers and 5,016,382 citations from 1893 to 2010. Our findings indicate that PageRank and Citation are statistically similar, both favoring older articles. However, Relevance excels in early forecasting, hence showing a weaker correlation with PageRank. Inspired by this, we introduce a new method called Structural-Temporal Rank (STRank). Validation experiments demonstrate that STRank excels in identifying milestone letters and predicting future impact, outperforming other methods in these tasks. This study introduces the idea of fusing structural and temporal information in designing ranking methods that could guide the future development of more efficient node identification algorithms in networks.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"33 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we develop the Jacobi spectral multi-Galerkin method alongside the Kumar-Sloan technique to approximate systems of non-linear Volterra Hammerstein integral equations. We conduct a comprehensive superconvergence analysis for both smooth and weakly singular kernels in both infinity and weighted-L2 norms. Our findings include the derivation of superconvergence rates for the multi-Galerkin method without resorting to iterated versions. Notably, our conclusions highlight the enhanced performance of multi-Galerkin approximation compared to Jacobi spectral Galerkin methods, while maintaining the same system size for both Jacobi spectral multi-Galerkin and Galerkin methods. To validate the robustness and efficiency of our theoretical results, numerical examples are provided.
{"title":"Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations","authors":"Samiran Chakraborty, Shivam Kumar Agrawal, Gnaneshwar Nelakanti","doi":"10.1016/j.chaos.2025.116008","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116008","url":null,"abstract":"In this article, we develop the Jacobi spectral multi-Galerkin method alongside the Kumar-Sloan technique to approximate systems of non-linear Volterra Hammerstein integral equations. We conduct a comprehensive superconvergence analysis for both smooth and weakly singular kernels in both infinity and weighted-<mml:math altimg=\"si871.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> norms. Our findings include the derivation of superconvergence rates for the multi-Galerkin method without resorting to iterated versions. Notably, our conclusions highlight the enhanced performance of multi-Galerkin approximation compared to Jacobi spectral Galerkin methods, while maintaining the same system size for both Jacobi spectral multi-Galerkin and Galerkin methods. To validate the robustness and efficiency of our theoretical results, numerical examples are provided.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"81 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-19DOI: 10.1016/j.chaos.2025.116014
Khursheed Muhammad, Mahnoor Sarfraz, N. Ameer Ahammad, Ibrahim E. Elseesy
Hybrid nanofluids exhibit enhanced thermal and transport properties due to synergistic interactions between their constituent materials. In this study, we present a novel investigation into the flow characteristics of a hybrid nanofluid surrounding a stretching cylinder. Our approach involves integrating molybdenum disulfide and copper nanoparticles into a water-based fluid. It considers stretching along the z-axis and delves into heat transfer and statistical aspects while accounting for thermal radiation and Joule heating effects and assuming negligible dissipation effects. Moreover, the hybrid nanofluid permeates a positioned porous medium above the cylinder. The article contributes to a deeper understanding of mixed nanofluid behavior and heat transfer within intricate conditions, ultimately aiding in the optimization and design of diverse engineering and industrial processes. Observations display a substantial decrease in energy and flow field attributes as a result of thermal and velocity slip effects. Also, the thermal radiation augments the energy transport and Nusselt number significantly.
{"title":"Improving thermal efficiency through Cu-MoS2 hybrid nanomaterials: A numerical and statistical approach","authors":"Khursheed Muhammad, Mahnoor Sarfraz, N. Ameer Ahammad, Ibrahim E. Elseesy","doi":"10.1016/j.chaos.2025.116014","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116014","url":null,"abstract":"Hybrid nanofluids exhibit enhanced thermal and transport properties due to synergistic interactions between their constituent materials. In this study, we present a novel investigation into the flow characteristics of a hybrid nanofluid surrounding a stretching cylinder. Our approach involves integrating molybdenum disulfide and copper nanoparticles into a water-based fluid. It considers stretching along the <ce:italic>z</ce:italic>-axis and delves into heat transfer and statistical aspects while accounting for thermal radiation and Joule heating effects and assuming negligible dissipation effects. Moreover, the hybrid nanofluid permeates a positioned porous medium above the cylinder. The article contributes to a deeper understanding of mixed nanofluid behavior and heat transfer within intricate conditions, ultimately aiding in the optimization and design of diverse engineering and industrial processes. Observations display a substantial decrease in energy and flow field attributes as a result of thermal and velocity slip effects. Also, the thermal radiation augments the energy transport and Nusselt number significantly.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"38 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-18DOI: 10.1016/j.chaos.2025.115994
Fengde Chen, Zhong Li, Qin Pan, Qun Zhu
In this paper, we study a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges. It is shown that the model can undergo a cusp type degenerate Bogdanov–Takens bifurcation of codimension 4, focus and elliptic types degenerate Bogdanov–Takens bifurcations of codimension 3, and degenerate Hopf bifurcation of codimension 3 as the parameters vary. The model can exhibit the coexistence of multiple positive steady states, multiple limit cycles, and homoclinic loops. Our results indicate that a larger prey refuge contributes to the coexistence of both species. Numerical simulations, including three limit cycles, quadristability, a large-amplitude limit cycle enclosing three positive steady states and a homoclinic loop, two large-amplitude limit cycles enclosing three positive steady states, are presented to illustrate the theoretical results.
{"title":"Bifurcations in a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges","authors":"Fengde Chen, Zhong Li, Qin Pan, Qun Zhu","doi":"10.1016/j.chaos.2025.115994","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.115994","url":null,"abstract":"In this paper, we study a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges. It is shown that the model can undergo a cusp type degenerate Bogdanov–Takens bifurcation of codimension 4, focus and elliptic types degenerate Bogdanov–Takens bifurcations of codimension 3, and degenerate Hopf bifurcation of codimension 3 as the parameters vary. The model can exhibit the coexistence of multiple positive steady states, multiple limit cycles, and homoclinic loops. Our results indicate that a larger prey refuge contributes to the coexistence of both species. Numerical simulations, including three limit cycles, quadristability, a large-amplitude limit cycle enclosing three positive steady states and a homoclinic loop, two large-amplitude limit cycles enclosing three positive steady states, are presented to illustrate the theoretical results.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"45 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-18DOI: 10.1016/j.chaos.2025.116018
Zhao-Li Shen, Yue-Hao Jiao, Yi-Kun Wei, Chun Wen, Bruno Carpentieri
Quantifying node centrality in multilayer networks is crucial for identifying influential nodes across various applications. Building on the PageRank model for single-layer networks, Lv et al. recently introduced a promising multilayer PageRank model for assessing node and layer centrality. In this paper, we reformulate this model within a discrete Markov chain framework. Our approach incorporates link diversity to enhance centrality measurement and ensures irreducibility within the internal Markov chains. This refinement enables an efficient computational strategy leveraging numerical algebra techniques. Experiments across diverse multilayer networks demonstrate the model’s effectiveness and computational efficiency, particularly for large-scale networks.
{"title":"Efficient hybrid PageRank centrality computation for multilayer networks","authors":"Zhao-Li Shen, Yue-Hao Jiao, Yi-Kun Wei, Chun Wen, Bruno Carpentieri","doi":"10.1016/j.chaos.2025.116018","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116018","url":null,"abstract":"Quantifying node centrality in multilayer networks is crucial for identifying influential nodes across various applications. Building on the PageRank model for single-layer networks, Lv et al. recently introduced a promising multilayer PageRank model for assessing node and layer centrality. In this paper, we reformulate this model within a discrete Markov chain framework. Our approach incorporates link diversity to enhance centrality measurement and ensures irreducibility within the internal Markov chains. This refinement enables an efficient computational strategy leveraging numerical algebra techniques. Experiments across diverse multilayer networks demonstrate the model’s effectiveness and computational efficiency, particularly for large-scale networks.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"51 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-18DOI: 10.1016/j.chaos.2025.116010
Z. Mahmoudi, M. Mehdizadeh Khalsaraei, M. Nosrati Sahlan, A. Shokri
The mechanical properties of the various materials could be influenced by external forces. The aim of this paper is to study the fractional order of viscoelastic column dynamic in Caputo sense. For this purpose, Laguerre wavelets and their operational matrices of integer and fractional orders are constructed and utilized to reduce the main fractional problem to some algebraic equation. Then, the obtained equation is discretized in the determined collocation nodes. Therefore an algebraic system is achieved that by solving it, the approximated solution of main problem is obtained. For showing the accuracy and efficiency of the purposed method, some illustrative examples are provided and the numerical results are compared with the results of some other approaches.
{"title":"Laguerre wavelets spectral method for solving a class of fractional order PDEs arising in viscoelastic column modeling","authors":"Z. Mahmoudi, M. Mehdizadeh Khalsaraei, M. Nosrati Sahlan, A. Shokri","doi":"10.1016/j.chaos.2025.116010","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116010","url":null,"abstract":"The mechanical properties of the various materials could be influenced by external forces. The aim of this paper is to study the fractional order of viscoelastic column dynamic in Caputo sense. For this purpose, Laguerre wavelets and their operational matrices of integer and fractional orders are constructed and utilized to reduce the main fractional problem to some algebraic equation. Then, the obtained equation is discretized in the determined collocation nodes. Therefore an algebraic system is achieved that by solving it, the approximated solution of main problem is obtained. For showing the accuracy and efficiency of the purposed method, some illustrative examples are provided and the numerical results are compared with the results of some other approaches.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"1 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-18DOI: 10.1016/j.chaos.2025.116009
Priyanka Harjule, Rinki Sharma, Rajesh Kumar
This article proposes a modified fractional gradient descent algorithm to enhance the learning capabilities of neural networks, comprising the benefits of a metaheuristic optimizer. The use of fractional derivatives, which possess memory properties, offers an additional degree of adaptability to the network. The convergence of the fractional gradient descent algorithm, incorporating the Caputo derivative in the neural network’s backpropagation process, is thoroughly examined, and a detailed convergence analysis is provided which indicates that it enables a more gradual and controlled adaptation of the network to the data. Additionally, the optimal fractional order has been found for each dataset, a contribution that has not been previously explored in the literature, which has a significant impact on the training of neural networks with fractional gradient backpropagation. In the experiments, four classification datasets and one regression dataset were used, and the results consistently show that the proposed hybrid algorithm achieves faster convergence across all cases. The empirical results with the proposed algorithm are supported by theoretical convergence analysis. Empirical results demonstrate that the proposed optimizer with optimal order yields more accurate results compared to existing optimizers.
{"title":"Fractional-order gradient approach for optimizing neural networks: A theoretical and empirical analysis","authors":"Priyanka Harjule, Rinki Sharma, Rajesh Kumar","doi":"10.1016/j.chaos.2025.116009","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116009","url":null,"abstract":"This article proposes a modified fractional gradient descent algorithm to enhance the learning capabilities of neural networks, comprising the benefits of a metaheuristic optimizer. The use of fractional derivatives, which possess memory properties, offers an additional degree of adaptability to the network. The convergence of the fractional gradient descent algorithm, incorporating the Caputo derivative in the neural network’s backpropagation process, is thoroughly examined, and a detailed convergence analysis is provided which indicates that it enables a more gradual and controlled adaptation of the network to the data. Additionally, the optimal fractional order has been found for each dataset, a contribution that has not been previously explored in the literature, which has a significant impact on the training of neural networks with fractional gradient backpropagation. In the experiments, four classification datasets and one regression dataset were used, and the results consistently show that the proposed hybrid algorithm achieves faster convergence across all cases. The empirical results with the proposed algorithm are supported by theoretical convergence analysis. Empirical results demonstrate that the proposed optimizer with optimal order yields more accurate results compared to existing optimizers.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"12 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021200","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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