Pub Date : 2024-12-20DOI: 10.1016/j.cnsns.2024.108564
Kaijie Chen, Zhijun Li, Yang Yin
The normal functioning of the actual brain relies on the collaborative efforts of neurons across multiple functional regions as well as the support and regulation of astrocytes, and its operating environment is both intricate and diverse. Hence, to replicate the electrophysiological properties of the central nervous system more accurately, it is essential to take the neuronal heterogeneity, the role of astrocytes, and environmental effects into account together. To this end, a neuron–astrocyte network comprising an Hindmarsh-Rose (HR) neuron, a FitzHugh-Nagumo (FHN) neuron, and an astrocyte, is proposed in this paper. The network is subjected to a complex environment to mimic the neural firing activities in biological reality. Several numerical analyses are performed to reveal the effects of the environments on the firing activities and the role of the astrocyte on the heterogeneous neuron network. It is found that the astrocyte can reduce coupling strength through neurotransmitter transmission, allowing for real-time regulation of coupling strength between neurons. More interestingly, environmental changes can alter the firing patterns of the neuron–astrocyte network, and greater electromagnetic radiation intensity and higher temperature may contribute to the firing synchronization between the coupled neurons. Finally, a hardware implementation based on the DSP platform is constructed to verify the correctness and feasibility of the neuron–astrocyte network under the interference of complex environment.
{"title":"Neural activities of neuron–Astrocyte network under environmental disturbances: Numerical analysis and hardware experiments","authors":"Kaijie Chen, Zhijun Li, Yang Yin","doi":"10.1016/j.cnsns.2024.108564","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108564","url":null,"abstract":"The normal functioning of the actual brain relies on the collaborative efforts of neurons across multiple functional regions as well as the support and regulation of astrocytes, and its operating environment is both intricate and diverse. Hence, to replicate the electrophysiological properties of the central nervous system more accurately, it is essential to take the neuronal heterogeneity, the role of astrocytes, and environmental effects into account together. To this end, a neuron–astrocyte network comprising an Hindmarsh-Rose (HR) neuron, a FitzHugh-Nagumo (FHN) neuron, and an astrocyte, is proposed in this paper. The network is subjected to a complex environment to mimic the neural firing activities in biological reality. Several numerical analyses are performed to reveal the effects of the environments on the firing activities and the role of the astrocyte on the heterogeneous neuron network. It is found that the astrocyte can reduce coupling strength through neurotransmitter transmission, allowing for real-time regulation of coupling strength between neurons. More interestingly, environmental changes can alter the firing patterns of the neuron–astrocyte network, and greater electromagnetic radiation intensity and higher temperature may contribute to the firing synchronization between the coupled neurons. Finally, a hardware implementation based on the DSP platform is constructed to verify the correctness and feasibility of the neuron–astrocyte network under the interference of complex environment.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"113 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-20DOI: 10.1016/j.cnsns.2024.108541
Xincheng Zhuang, Yang Tian, Haoping Wang, Sofiane Ahmed-Ali
This study presents a novel event-triggered joint adaptive high-gain observer design for delayed output-sampled nonlinear systems with output injection. These systems are characterized by the presence of unknown parameters that influence both the state and output equations. The major difficulty in designing the observer lies in the interplay between event-triggered mechanism, output injection, and time-varying delays. Additionally, the non-affine nature of the parameter’s entry into the system states equation further complicates the design. To address these challenges, a new adaptive law for unknown parameter estimation is developed under delay measurement. A novel non-Zeno dynamic event-triggered mechanism coupled with a closed-loop output predictor is proposed. The resulting observer exhibits two main features: the first one provides an input-to-state stable property, and the second one is the establishment of a theoretical condition for the inter-event time of the proposed dynamic event-triggered mechanism. The effectiveness of the designed observer is demonstrated through numerical simulations and performance comparisons with previous works.
{"title":"Event-triggered joint adaptive high-gain observer design for delayed output-sampled nonlinear systems with unknown parameters and output injection","authors":"Xincheng Zhuang, Yang Tian, Haoping Wang, Sofiane Ahmed-Ali","doi":"10.1016/j.cnsns.2024.108541","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108541","url":null,"abstract":"This study presents a novel event-triggered joint adaptive high-gain observer design for delayed output-sampled nonlinear systems with output injection. These systems are characterized by the presence of unknown parameters that influence both the state and output equations. The major difficulty in designing the observer lies in the interplay between event-triggered mechanism, output injection, and time-varying delays. Additionally, the non-affine nature of the parameter’s entry into the system states equation further complicates the design. To address these challenges, a new adaptive law for unknown parameter estimation is developed under delay measurement. A novel non-Zeno dynamic event-triggered mechanism coupled with a closed-loop output predictor is proposed. The resulting observer exhibits two main features: the first one provides an input-to-state stable property, and the second one is the establishment of a theoretical condition for the inter-event time of the proposed dynamic event-triggered mechanism. The effectiveness of the designed observer is demonstrated through numerical simulations and performance comparisons with previous works.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"23 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-20DOI: 10.1016/j.cnsns.2024.108560
Xiaoqiang Guo, Zhichen Qiu, Mingming Li, Xinye Li, Ning Hu, Libin Zhao, Chengyang Ye
In response to the failure problem of axial-torsional coupling vibration of drill string in oil & gas wells, an axial-torsional coupling nonlinear vibration model of drill string is established using the finite element method, which can effectively simulate the coupling vibration of actual wellbore drill string multi-body systems and the real-time rock breaking effect. Moreover, the correctness and effectiveness of the theoretical model verified by a similar experiment of tubing vibration. Finally, the influences of feed rate and rotary drilling speed on the nonlinear behavior of the vibration of the drill string are investigated. The results obtained demonstrate that, the axial vibration response of the drill string system shows an overall trend of quasi-periodic-chaotic change with the increase of feed rate, and the torsional vibration of the drill string shows the trend of quasi periodic-chaotic. When the feed rate is high, the vibration of the drill string system is mainly for the irregular and complex hybrid motion. Therefore, the appropriate reduction of feed speed can increase the stability of the drill string on-site, and reduce the jump drilling and stick-slip vibration of the drill string. When the rotary drilling speed is 90–210 rpm, the torsional vibration response of the drill string shows a chaotic-quasi-periodic trend and the complexity of the torsional vibration of the drill string decreases with the increase of rotary drilling speed. The axial vibration response of the drill string shows a chaotic-quasi-periodic-chaotic trend with the increase of the rotary drilling speed. When the rotary drilling speed increases to 400–410 rpm, the axial vibration of the drill string becomes a quasi-periodic motion. Therefore, increasing the rotary drilling speed within a certain range can reduce the complexity of the vibration of the drill string and reduce the skip and stick-slip vibration of the drill string.
{"title":"Axial-torsional coupling vibration model and nonlinear behavior of drill string system in oil and gas wells","authors":"Xiaoqiang Guo, Zhichen Qiu, Mingming Li, Xinye Li, Ning Hu, Libin Zhao, Chengyang Ye","doi":"10.1016/j.cnsns.2024.108560","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108560","url":null,"abstract":"In response to the failure problem of axial-torsional coupling vibration of drill string in oil & gas wells, an axial-torsional coupling nonlinear vibration model of drill string is established using the finite element method, which can effectively simulate the coupling vibration of actual wellbore drill string multi-body systems and the real-time rock breaking effect. Moreover, the correctness and effectiveness of the theoretical model verified by a similar experiment of tubing vibration. Finally, the influences of feed rate and rotary drilling speed on the nonlinear behavior of the vibration of the drill string are investigated. The results obtained demonstrate that, the axial vibration response of the drill string system shows an overall trend of quasi-periodic-chaotic change with the increase of feed rate, and the torsional vibration of the drill string shows the trend of quasi periodic-chaotic. When the feed rate is high, the vibration of the drill string system is mainly for the irregular and complex hybrid motion. Therefore, the appropriate reduction of feed speed can increase the stability of the drill string on-site, and reduce the jump drilling and stick-slip vibration of the drill string. When the rotary drilling speed is 90–210 rpm, the torsional vibration response of the drill string shows a chaotic-quasi-periodic trend and the complexity of the torsional vibration of the drill string decreases with the increase of rotary drilling speed. The axial vibration response of the drill string shows a chaotic-quasi-periodic-chaotic trend with the increase of the rotary drilling speed. When the rotary drilling speed increases to 400–410 rpm, the axial vibration of the drill string becomes a quasi-periodic motion. Therefore, increasing the rotary drilling speed within a certain range can reduce the complexity of the vibration of the drill string and reduce the skip and stick-slip vibration of the drill string.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"41 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-20DOI: 10.1016/j.cnsns.2024.108558
Amir Najibi, Parisa Alizadeh
We present a nonlinear numerical study of the two-dimensional functionally graded porosity (2D-FGP) transient thermo-elastic problem for the infinite cylinder sector with temperature-dependent material properties. The paper employs a higher-order graded finite element method (graded-FEM) to develop the problem and determines the effective values of the 2D material properties using the Kerner micromechanical model. The sequentially coupled nonlinear thermo-elastic problem is solved by an implicit time-marching technique, and the validity of graded FEM using the cell-vertex finite volume method (CV-FVM) is assessed. Then the effects of material and porosity distributions on the temperature, displacement, stresses, and strength of the 2D-FGP plane strain cylinder sector are thoroughly investigated. The findings show that porosity has a smaller impact on normalized effective stresses (NES) than material distribution, as evidenced by higher NES values in the cylinder sector without porosity and the ZrO2 rich cylinder has the lowest NES value. Despite a temperature difference of only 8∘K, the cylinder with no porosity distribution has 56%, 48%, 68%, and 60% higher radial, hoop, axial, and von Mises stresses than the cylinder with a quadratic porosity distribution. At the specific point, higher porosity at nr=nθ=1 compared to nr=nθ=2 resulted in a 5∘K temperature decrease and correspondingly lower stresses, indicating that the structure's porosity reduced the effective stress. Because thermal stress is highly sensitive to constituents and porosity distributions, optimizing the parameters is critical to having the most effective stress reductions.
{"title":"Nonlinear transient thermal stress investigation of 2D-FG porosity long cylinder sector","authors":"Amir Najibi, Parisa Alizadeh","doi":"10.1016/j.cnsns.2024.108558","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108558","url":null,"abstract":"We present a nonlinear numerical study of the two-dimensional functionally graded porosity (2D-FGP) transient thermo-elastic problem for the infinite cylinder sector with temperature-dependent material properties. The paper employs a higher-order graded finite element method (graded-FEM) to develop the problem and determines the effective values of the 2D material properties using the Kerner micromechanical model. The sequentially coupled nonlinear thermo-elastic problem is solved by an implicit time-marching technique, and the validity of graded FEM using the cell-vertex finite volume method (CV-FVM) is assessed. Then the effects of material and porosity distributions on the temperature, displacement, stresses, and strength of the 2D-FGP plane strain cylinder sector are thoroughly investigated. The findings show that porosity has a smaller impact on normalized effective stresses (NES) than material distribution, as evidenced by higher NES values in the cylinder sector without porosity and the ZrO2 rich cylinder has the lowest NES value. Despite a temperature difference of only <mml:math altimg=\"si22.svg\"><mml:mrow><mml:msup><mml:mn>8</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mi>K</mml:mi></mml:mrow></mml:math>, the cylinder with no porosity distribution has 56%, 48%, 68%, and 60% higher radial, hoop, axial, and von Mises stresses than the cylinder with a quadratic porosity distribution. At the specific point, higher porosity at <mml:math altimg=\"si23.svg\"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mo linebreak=\"goodbreak\">=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>θ</mml:mi></mml:msub><mml:mo linebreak=\"goodbreak\">=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> compared to <mml:math altimg=\"si24.svg\"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mo linebreak=\"goodbreak\">=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>θ</mml:mi></mml:msub><mml:mo linebreak=\"goodbreak\">=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> resulted in a <mml:math altimg=\"si25.svg\"><mml:mrow><mml:msup><mml:mn>5</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mi>K</mml:mi></mml:mrow></mml:math> temperature decrease and correspondingly lower stresses, indicating that the structure's porosity reduced the effective stress. Because thermal stress is highly sensitive to constituents and porosity distributions, optimizing the parameters is critical to having the most effective stress reductions.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"27 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-20DOI: 10.1016/j.cnsns.2024.108553
Sergey V. Stasenko, Alexander N. Kirdin
Systems with predetermined Lyapunov functions play an important role in many areas of applied mathematics, physics and engineering: dynamic optimization methods (objective functions and their modifications), machine learning (loss functions), thermodynamics and kinetics (free energy and other thermodynamic potentials), adaptive control (various objective functions, stabilization quality criteria and other Lyapunov functions). Dimensionality reduction is one of the main challenges in the modern era of big data and big models. Dimensionality reduction for systems with Lyapunov functions requires preserving dissipativity: the reduced system must also have a Lyapunov function, which is expected to be a restriction of the original Lyapunov function on the manifold of the reduced motion. An additional complexity of the problem is that the equations of motion themselves are often unknown in detail in advance and must be determined in the course of the study, while the Lyapunov function could be determined based on incomplete data. Therefore, the projection problem arises: for a given Lyapunov function, find a field of projectors such that the reduction of any dissipative system is again a dissipative system. In this paper, we present an explicit construction of such projectors and prove their uniqueness. We have also taken the first step beyond the approximation by manifolds. This is required in many applications. For this purpose, we introduce the concept of monotone trees and find a projection of dissipative systems onto monotone trees that preserves dissipativity.
{"title":"Preservation of dissipativity in dimensionality reduction","authors":"Sergey V. Stasenko, Alexander N. Kirdin","doi":"10.1016/j.cnsns.2024.108553","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108553","url":null,"abstract":"Systems with predetermined Lyapunov functions play an important role in many areas of applied mathematics, physics and engineering: dynamic optimization methods (objective functions and their modifications), machine learning (loss functions), thermodynamics and kinetics (free energy and other thermodynamic potentials), adaptive control (various objective functions, stabilization quality criteria and other Lyapunov functions). Dimensionality reduction is one of the main challenges in the modern era of big data and big models. Dimensionality reduction for systems with Lyapunov functions requires <ce:italic>preserving dissipativity</ce:italic>: the reduced system must also have a Lyapunov function, which is expected to be a restriction of the original Lyapunov function on the manifold of the reduced motion. An additional complexity of the problem is that the equations of motion themselves are often unknown in detail in advance and must be determined in the course of the study, while the Lyapunov function could be determined based on incomplete data. Therefore, the projection problem arises: for a given Lyapunov function, find a field of projectors such that the reduction of <ce:italic>any</ce:italic> dissipative system is again a dissipative system. In this paper, we present an explicit construction of such projectors and prove their uniqueness. We have also taken the first step beyond the approximation by manifolds. This is required in many applications. For this purpose, we introduce the concept of monotone trees and find a projection of dissipative systems onto monotone trees that preserves dissipativity.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"34 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-20DOI: 10.1016/j.cnsns.2024.108546
Feifei Chen, Xiaoting Rui, Hehua Ju, Guoping Wang, Kaimeng Wang
Robotic arms with high precision play a crucial role in industries like aerospace and intelligent manufacturing. Currently, industrial robotic arms typically adopt spherical wrists to obtain analytical solutions; however, manufacturing-related structural errors significantly reduce the end effector's absolute positioning accuracy, impeding the development towards high-precision autonomous control. This study presents a series of kinematic modelling, configuration design, and analytical inverse solutions for robotic arms with the goal of delivering precise and effective inverse kinematic solutions, while taking the engineering limitation into consideration. Taking the vector polynomial system as the key premise, an iterative kinematic model with the fewest number of equations, independent variables, and orders of magnitude is then established. Through decoupling analysis of the position and attitude in the kinematic model, configuration designs of robotic arms with orthogonal or parallel axes are proposed without adhering to the restrictions of three-axis intersection. Additionally, the inverse kinematic issue is addressed by conversion into polynomial space using the Dixon elimination approach. Eight sets of inverse kinematic solutions are obtained for any reachable position and attitude in simulation. The computation time does not exceed 2 milliseconds, and both position and attitude relative errors are below 10–15, enhancing computational accuracy for robot kinematics. The work of this paper provides a practical kinematic theory for the development of robotic arms with high absolute positioning accuracy and efficiency.
{"title":"Vector polynomial based analytical inverse kinematics and configuration design of 6R robotic arms","authors":"Feifei Chen, Xiaoting Rui, Hehua Ju, Guoping Wang, Kaimeng Wang","doi":"10.1016/j.cnsns.2024.108546","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108546","url":null,"abstract":"Robotic arms with high precision play a crucial role in industries like aerospace and intelligent manufacturing. Currently, industrial robotic arms typically adopt spherical wrists to obtain analytical solutions; however, manufacturing-related structural errors significantly reduce the end effector's absolute positioning accuracy, impeding the development towards high-precision autonomous control. This study presents a series of kinematic modelling, configuration design, and analytical inverse solutions for robotic arms with the goal of delivering precise and effective inverse kinematic solutions, while taking the engineering limitation into consideration. Taking the vector polynomial system as the key premise, an iterative kinematic model with the fewest number of equations, independent variables, and orders of magnitude is then established. Through decoupling analysis of the position and attitude in the kinematic model, configuration designs of robotic arms with orthogonal or parallel axes are proposed without adhering to the restrictions of three-axis intersection. Additionally, the inverse kinematic issue is addressed by conversion into polynomial space using the Dixon elimination approach. Eight sets of inverse kinematic solutions are obtained for any reachable position and attitude in simulation. The computation time does not exceed 2 milliseconds, and both position and attitude relative errors are below 10<ce:sup loc=\"post\">–15</ce:sup>, enhancing computational accuracy for robot kinematics. The work of this paper provides a practical kinematic theory for the development of robotic arms with high absolute positioning accuracy and efficiency.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"32 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The inverse eigenvalue problem of weighted Helmholtz equations is investigated. The density function is recovered from the observation of the limited spectral data. It is reformulated as an optimization problem and a multi-objective loss function is defined accordingly. A multi-artificial neural network (multi-ANN) algorithm is proposed. The existence and stability of the solution of the optimization problem, and the convergence of the multi-ANN solution towards that of the original optimization problem are proved. The numerical results of one-dimensional and two-dimensional inverse eigenvalue problems of the weighted Helmholtz equation are given. Compared with the traditional finite element method, the robustness and effectiveness of the proposed multi-ANN method are illustrated.
{"title":"Multi-artificial neural network for inverse eigenvalue problem with the weighted Helmholtz equation","authors":"Zhengfang Zhang, Shizhong Zou, Xihao Zhou, Xinping Shao, Mingyan He, Weifeng Chen","doi":"10.1016/j.cnsns.2024.108544","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108544","url":null,"abstract":"The inverse eigenvalue problem of weighted Helmholtz equations is investigated. The density function is recovered from the observation of the limited spectral data. It is reformulated as an optimization problem and a multi-objective loss function is defined accordingly. A multi-artificial neural network (multi-ANN) algorithm is proposed. The existence and stability of the solution of the optimization problem, and the convergence of the multi-ANN solution towards that of the original optimization problem are proved. The numerical results of one-dimensional and two-dimensional inverse eigenvalue problems of the weighted Helmholtz equation are given. Compared with the traditional finite element method, the robustness and effectiveness of the proposed multi-ANN method are illustrated.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"45 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-19DOI: 10.1016/j.cnsns.2024.108540
Qiu Peng, Siman Lin, Manchun Tan
In this paper, the finite-time synchronization (FTS) problem of fractional-order multiplex networks with internal delay, intra- and inter-layer coupling delays, and uncertain intra- and inter-layer coupling matrices is studied. A new hybrid controller, composed of an impulsive controller and a quantized controller, is designed to achieve FTS for the considered network in order to save control resources and reduce the burden of the network. Based on the fractional-order Lyapunov function method, utilizing the fractional-order impulsive finite-time inequality and other inequality methods, several fresh sufficient conditions for the synchronization of the fractional-order uncertain multiplex network (FOUMN) with multiple time-varying delays in an explicitly estimated finite time are obtained. These sufficient criteria also reflect that the FTS of the network is related to its topology, quantization parameters, the order of the fractional derivative, and the impulse function. Lastly, two numerical examples confirm that the theoretical findings are valid.
{"title":"Quantized hybrid impulsive control for finite-time synchronization of fractional-order uncertain multiplex networks with multiple time-varying delays","authors":"Qiu Peng, Siman Lin, Manchun Tan","doi":"10.1016/j.cnsns.2024.108540","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108540","url":null,"abstract":"In this paper, the finite-time synchronization (FTS) problem of fractional-order multiplex networks with internal delay, intra- and inter-layer coupling delays, and uncertain intra- and inter-layer coupling matrices is studied. A new hybrid controller, composed of an impulsive controller and a quantized controller, is designed to achieve FTS for the considered network in order to save control resources and reduce the burden of the network. Based on the fractional-order Lyapunov function method, utilizing the fractional-order impulsive finite-time inequality and other inequality methods, several fresh sufficient conditions for the synchronization of the fractional-order uncertain multiplex network (FOUMN) with multiple time-varying delays in an explicitly estimated finite time are obtained. These sufficient criteria also reflect that the FTS of the network is related to its topology, quantization parameters, the order of the fractional derivative, and the impulse function. Lastly, two numerical examples confirm that the theoretical findings are valid.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"62 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-19DOI: 10.1016/j.cnsns.2024.108538
Adrián P. Bustamante
We consider a Froeschlé map and we add a weak dissipation proportional to ɛ3, where ɛ is the parameter of perturbation. We compute formal expansions of lower dimensional tori, both in the conservative and weakly dissipatives cases, and use them to estimate the shape of their domains of analyticity with respect to ɛ. Our results support conjectures in the literature.
{"title":"Computation of domains of analyticity of lower dimensional tori in a weakly dissipative Froeschlé map","authors":"Adrián P. Bustamante","doi":"10.1016/j.cnsns.2024.108538","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108538","url":null,"abstract":"We consider a Froeschlé map and we add a weak dissipation proportional to <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>ɛ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>, where <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mi>ɛ</mml:mi></mml:math> is the parameter of perturbation. We compute formal expansions of lower dimensional tori, both in the conservative and weakly dissipatives cases, and use them to estimate the shape of their domains of analyticity with respect to <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mi>ɛ</mml:mi></mml:math>. Our results support conjectures in the literature.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"20 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-19DOI: 10.1016/j.cnsns.2024.108543
Isaac A. García, Jaume Giné, Jaume Llibre
In this work we focus in the family of real planar polynomial vector fields of arbitrary degree. We are interested in to characterize when a (local) center singularity of these vector fields becomes a global center, that is, its period annulus foliates the punctured real plane. The characterization of any global center is done by blowing-down the polycycle at infinity into a monodromic singular point.
{"title":"Characterization of global centers by the monodromy at infinity","authors":"Isaac A. García, Jaume Giné, Jaume Llibre","doi":"10.1016/j.cnsns.2024.108543","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108543","url":null,"abstract":"In this work we focus in the family of real planar polynomial vector fields of arbitrary degree. We are interested in to characterize when a (local) center singularity of these vector fields becomes a global center, that is, its period annulus foliates the punctured real plane. The characterization of any global center is done by blowing-down the polycycle at infinity into a monodromic singular point.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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