Pub Date : 2025-01-01DOI: 10.1016/j.cnsns.2024.108571
Lulu Xu, Juan Yu, Cheng Hu
In practical applications, loads of single complex network models cannot meet the research requirements owing to the interaction between network layers. Furthermore, the measurability of state information is rather difficult in the light of some uncontrollable factors. In view of these facts, we are mainly devoted to researching the output synchronization problem of fractional-order multi-layer network with output coupling under stochastic deceptive attacks. By utilizing the Lyapunov function, graph theoretic, and LMI techniques, some sufficient criteria are introduced to achieve output synchronization. Firstly, a quantized pinning scheme is designed to discuss the output synchronization of fractional-order multi-layer networks in the absence of cyber attacks. Subsequently, in view of the fact that fractional-order multi-layer networks are susceptible to malicious attacks of stochastic networks in synchronization process, an adaptive quantized pinning control strategy is developed. This strategy can adjust its personal parameters according to the state changes of nodes. Especially, the output matrix is no more restricted to a diagonal matrix, and the relationship between the output matrix and output synchronization is further acquired, which increases the applicability of controlled system. Ultimately, two persuasive numerical examples are used to expound the availability and superiority of theoretical results.
{"title":"Output synchronization of fractional-order multi-layer network via quantized pinning control under stochastic cyber attacks","authors":"Lulu Xu, Juan Yu, Cheng Hu","doi":"10.1016/j.cnsns.2024.108571","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108571","url":null,"abstract":"In practical applications, loads of single complex network models cannot meet the research requirements owing to the interaction between network layers. Furthermore, the measurability of state information is rather difficult in the light of some uncontrollable factors. In view of these facts, we are mainly devoted to researching the output synchronization problem of fractional-order multi-layer network with output coupling under stochastic deceptive attacks. By utilizing the Lyapunov function, graph theoretic, and LMI techniques, some sufficient criteria are introduced to achieve output synchronization. Firstly, a quantized pinning scheme is designed to discuss the output synchronization of fractional-order multi-layer networks in the absence of cyber attacks. Subsequently, in view of the fact that fractional-order multi-layer networks are susceptible to malicious attacks of stochastic networks in synchronization process, an adaptive quantized pinning control strategy is developed. This strategy can adjust its personal parameters according to the state changes of nodes. Especially, the output matrix is no more restricted to a diagonal matrix, and the relationship between the output matrix and output synchronization is further acquired, which increases the applicability of controlled system. Ultimately, two persuasive numerical examples are used to expound the availability and superiority of theoretical results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"204 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142937626","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}
Identifying the most influential nodes has become a crucial topic in network science for applications such as viral marketing, rumor suppression, and disease control. However, traditional research on influential node identification focuses mainly on pairwise interactions rather than higher-order interactions between individuals. To solve this problem, we propose s-distance-based fuzzy centrality methods (HDF and EHDF) that are customized for hypergraphs, which can characterize higher-order interactions between nodes via hyperedges. The methods we proposed assume that the influence of a node is dependent on neighboring nodes with a certain s-distance. Extensive experiments on 6 empirical hypergraphs indicate that HDF and EHDF can better identify influential nodes than the baseline methods. Furthermore, our methods demonstrate significant effectiveness in identifying the most influential nodes, achieving a maximum improvement of 411.37% compared to the best state-of-the-art baseline. Our proposed theoretical framework for identifying influential nodes could provide insights into the utilization of higher-order structures for tasks such as vital node identification, influence maximization, and network dismantling.
{"title":"Locating influential nodes in hypergraphs via fuzzy collective influence","authors":"Su-Su Zhang, Xiaoyan Yu, Gui-Quan Sun, Chuang Liu, Xiu-Xiu Zhan","doi":"10.1016/j.cnsns.2024.108574","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108574","url":null,"abstract":"Identifying the most influential nodes has become a crucial topic in network science for applications such as viral marketing, rumor suppression, and disease control. However, traditional research on influential node identification focuses mainly on pairwise interactions rather than higher-order interactions between individuals. To solve this problem, we propose <mml:math altimg=\"si126.svg\" display=\"inline\"><mml:mi>s</mml:mi></mml:math>-distance-based fuzzy centrality methods (HDF and EHDF) that are customized for hypergraphs, which can characterize higher-order interactions between nodes via hyperedges. The methods we proposed assume that the influence of a node is dependent on neighboring nodes with a certain <mml:math altimg=\"si126.svg\" display=\"inline\"><mml:mi>s</mml:mi></mml:math>-distance. Extensive experiments on 6 empirical hypergraphs indicate that HDF and EHDF can better identify influential nodes than the baseline methods. Furthermore, our methods demonstrate significant effectiveness in identifying the most influential nodes, achieving a maximum improvement of 411.37% compared to the best state-of-the-art baseline. Our proposed theoretical framework for identifying influential nodes could provide insights into the utilization of higher-order structures for tasks such as vital node identification, influence maximization, and network dismantling.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"28 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936906","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 : 2024-12-30DOI: 10.1016/j.cnsns.2024.108588
Wei Zhang, Muchen Shi, Chaoran Liu, Xiaoyang Su
Vibrations are usually harmful in engineering and thus need to be mitigated, whereas they are also potential sources of useful energy and can be harnessed. Current difficulty in vibration mitigation and energy harvesting is to achieve both objectives synchronously, especially in low-frequency environments. In this paper, a device composed of quasi-zero-stiffness (QZS) pneumatic support and magnetic-piezoelectric cantilever beams is proposed for synchronous low-frequency vibration mitigation and energy harvesting. The pneumatic support enables the adaptability to different load masses while maintaining QZS. The magnetic spacing in the magnetic-piezoelectric cantilever beam can be adjusted to produce various stiffness properties, including nonlinear positive stiffness, QZS, and bistability. The nonlinear dynamic behaviors are studied and the performances are analyzed based on the electromechanical coupled equations. Results indicate that energy harvesting and vibration mitigation can be achieved at low frequencies, and most importantly the energy harvesting region is located within the vibration mitigation region, implying synchronization of the two objectives. Different situations induced by the bifurcation of magnetic spacing are studied and discussed. It is shown that the magnetic spacing that produces QZS for the cantilever beam is the best choice, and the energy harvesting region can be easily tuned by adjusting the magnetic spacing.
{"title":"Synchronous low-frequency vibration mitigation and energy harvesting with tunable load bearing capacity and operation band","authors":"Wei Zhang, Muchen Shi, Chaoran Liu, Xiaoyang Su","doi":"10.1016/j.cnsns.2024.108588","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108588","url":null,"abstract":"Vibrations are usually harmful in engineering and thus need to be mitigated, whereas they are also potential sources of useful energy and can be harnessed. Current difficulty in vibration mitigation and energy harvesting is to achieve both objectives synchronously, especially in low-frequency environments. In this paper, a device composed of quasi-zero-stiffness (QZS) pneumatic support and magnetic-piezoelectric cantilever beams is proposed for synchronous low-frequency vibration mitigation and energy harvesting. The pneumatic support enables the adaptability to different load masses while maintaining QZS. The magnetic spacing in the magnetic-piezoelectric cantilever beam can be adjusted to produce various stiffness properties, including nonlinear positive stiffness, QZS, and bistability. The nonlinear dynamic behaviors are studied and the performances are analyzed based on the electromechanical coupled equations. Results indicate that energy harvesting and vibration mitigation can be achieved at low frequencies, and most importantly the energy harvesting region is located within the vibration mitigation region, implying synchronization of the two objectives. Different situations induced by the bifurcation of magnetic spacing are studied and discussed. It is shown that the magnetic spacing that produces QZS for the cantilever beam is the best choice, and the energy harvesting region can be easily tuned by adjusting the magnetic spacing.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"16 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936908","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 : 2024-12-28DOI: 10.1016/j.cnsns.2024.108568
Jiake Sun, Junmin Wang
This paper investigates the boundary stabilization of time fractional-order ODE cascaded with time fractional-order diffusion-wave equation systems subject to external disturbance. We stabilize the systems by using sliding mode control method and backstepping method. We prove the existence of the generalized solution of the closed-loop systems by Galerkin’s method and successive approximation method. The Mittag-Leffler stability of the systems is proven by Lyapunov method. The numerical simulations are presented to illustrate the validity of the theoretical results.
{"title":"Boundary Mittag-Leffler stabilization and disturbance rejection for time fractional ODE diffusion-wave equation cascaded systems","authors":"Jiake Sun, Junmin Wang","doi":"10.1016/j.cnsns.2024.108568","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108568","url":null,"abstract":"This paper investigates the boundary stabilization of time fractional-order ODE cascaded with time fractional-order diffusion-wave equation systems subject to external disturbance. We stabilize the systems by using sliding mode control method and backstepping method. We prove the existence of the generalized solution of the closed-loop systems by Galerkin’s method and successive approximation method. The Mittag-Leffler stability of the systems is proven by Lyapunov method. The numerical simulations are presented to illustrate the validity of the theoretical results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"848 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911896","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}
As the temperature surpasses the threshold for the completion of austenitic transformation, shape memory alloys (SMAs) necessitate a substantial external force to trigger internal phase transformation. Given the substantial deformation induced by the external force on SMAs, the application of geometrically nonlinear analysis becomes essential. In this paper, reproducing kernel particle method (RKPM) is employed to investigate the geometrically nonlinear behavior of SMAs. The penalty function method is applied to impose the displacement boundary conditions. The study utilizes the Galerkin weak form with total Lagrangian (TL) framework to develop geometrically nonlinear SMAs equations, solved via Newton-Raphson (N-R) iteration. The effects of varying penalty factor and radius control parameter of the influence domain on error and computational stability are investigated. Ultimately, the suitability of applying RKPM for exploring the geometrically nonlinearity behavior of SMAs is demonstrated via numerical examples.
{"title":"The analysis of geometrically nonlinear behavior of SMAs using RKPM","authors":"Yijie Zhang, Gaofeng Wei, Tengda Liu, Fengfeng Hua, Shasha Zhou","doi":"10.1016/j.cnsns.2024.108581","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108581","url":null,"abstract":"As the temperature surpasses the threshold for the completion of austenitic transformation, shape memory alloys (SMAs) necessitate a substantial external force to trigger internal phase transformation. Given the substantial deformation induced by the external force on SMAs, the application of geometrically nonlinear analysis becomes essential. In this paper, reproducing kernel particle method (RKPM) is employed to investigate the geometrically nonlinear behavior of SMAs. The penalty function method is applied to impose the displacement boundary conditions. The study utilizes the Galerkin weak form with total Lagrangian (TL) framework to develop geometrically nonlinear SMAs equations, solved via Newton-Raphson (N-R) iteration. The effects of varying penalty factor and radius control parameter of the influence domain on error and computational stability are investigated. Ultimately, the suitability of applying RKPM for exploring the geometrically nonlinearity behavior of SMAs is demonstrated via numerical examples.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"31 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142937629","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 : 2024-12-28DOI: 10.1016/j.cnsns.2024.108569
Jakub Czwórnóg, Daniel Wilczak
Steady states of the Swift–Hohenberg (Swift and Hohenberg, 1977) equation are studied. For the associated four-dimensional ODE we prove that on the energy level E=0 two smooth branches of even periodic solutions are created through the saddle–node bifurcation. We also show that these orbits satisfy certain geometric properties, which implies that the system has positive topological entropy for an explicit and wide range of parameter values of the system.
研究了Swift - Hohenberg （Swift and Hohenberg, 1977）方程的稳态。对于相关的四维ODE，我们证明了在能级E=0上通过鞍节点分岔产生了两个偶周期解的光滑分支。我们还证明了这些轨道满足一定的几何性质，这意味着系统具有正的拓扑熵，对于系统的显式和大范围的参数值。
{"title":"Continuation and bifurcations of periodic orbits and symbolic dynamics in the Swift–Hohenberg equation","authors":"Jakub Czwórnóg, Daniel Wilczak","doi":"10.1016/j.cnsns.2024.108569","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108569","url":null,"abstract":"Steady states of the Swift–Hohenberg (Swift and Hohenberg, 1977) equation are studied. For the associated four-dimensional ODE we prove that on the energy level <mml:math altimg=\"si91.svg\" display=\"inline\"><mml:mrow><mml:mi>E</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> two smooth branches of even periodic solutions are created through the saddle–node bifurcation. We also show that these orbits satisfy certain geometric properties, which implies that the system has positive topological entropy for an explicit and wide range of parameter values of the system.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"41 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911895","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}
Research on system dynamics of friction stir welding (FSW) of aluminum alloy is of great significance to optimize the welding process and improve welding quality. In this paper, the aluminum alloy FSW is taken as the object, considering the influence of the arc value of the stirring pin, the feed quantity and the equivalent friction coefficient, the nonlinear dynamic model of the aluminum alloy FSW system is established, and the influence of different factors on the vibration characteristics of the system in x direction and y direction is explored. Time domain diagram, phase diagram, Poincaré diagram, bifurcation diagram and Lyapunov exponent are used to reveal the vibration response characteristics of the aluminum alloy FSW system. The time delay multi-scale method was used to study the main resonance characteristics of the aluminum alloy FSW system, and the effects of feed quantity and time delay parameters on the main resonance characteristics of the system were explored. The results show that the system shows strong nonlinearity when considering the value of the arc of the stirring pin, the feed quantity and the equivalent softening friction coefficient. With the increase of the feed quantity and the a^#mount of stirring pin, the vibration characteristics of the system change from single-cycle to multi-cycle to chaos. The system will be in a complex nonlinear state when the stirring pin is rotated into the radian value and the feed quantity is large. The system can be kept stable by adjusting the feed quantity and time delay parameters. The welding effect is good and the welding quality is high when the speed of FSW of aluminum alloy is about [800 (r/min),900 (r/min)] under the lower feed quantity and the arc value of the stirring pin.
{"title":"Nonlinear dynamic of friction stir welding for aluminum alloy","authors":"Shuai Mo, Yongjun Hu, Taojiang Huang, Yuansheng Zhou, Jielu Zhang, Wei Zhang","doi":"10.1016/j.cnsns.2024.108576","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108576","url":null,"abstract":"Research on system dynamics of friction stir welding (FSW) of aluminum alloy is of great significance to optimize the welding process and improve welding quality. In this paper, the aluminum alloy FSW is taken as the object, considering the influence of the arc value of the stirring pin, the feed quantity and the equivalent friction coefficient, the nonlinear dynamic model of the aluminum alloy FSW system is established, and the influence of different factors on the vibration characteristics of the system in <ce:italic>x</ce:italic> direction and <ce:italic>y</ce:italic> direction is explored. Time domain diagram, phase diagram, Poincaré diagram, bifurcation diagram and Lyapunov exponent are used to reveal the vibration response characteristics of the aluminum alloy FSW system. The time delay multi-scale method was used to study the main resonance characteristics of the aluminum alloy FSW system, and the effects of feed quantity and time delay parameters on the main resonance characteristics of the system were explored. The results show that the system shows strong nonlinearity when considering the value of the arc of the stirring pin, the feed quantity and the equivalent softening friction coefficient. With the increase of the feed quantity and the a^#mount of stirring pin, the vibration characteristics of the system change from single-cycle to multi-cycle to chaos. The system will be in a complex nonlinear state when the stirring pin is rotated into the radian value and the feed quantity is large. The system can be kept stable by adjusting the feed quantity and time delay parameters. The welding effect is good and the welding quality is high when the speed of FSW of aluminum alloy is about [800 (r/min),900 (r/min)] under the lower feed quantity and the arc value of the stirring pin.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"34 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911899","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}
Herringbone gears have been widely used in high-speed and heavy-duty fields such as ships, aerospace and automobiles due to their outstanding bearing capacity, high contact ratio, small axial force and stable transmission. Under the factors such as high speed and heavy load, the gear may crack at the root of the tooth, which affects the normal operation of the gear system. In this paper, the herringbone gear transmission system is taken as the research object, and the nonlinear dynamic model of the herringbone gear transmission system considering cracks is established under various excitation factors. According to the potential energy method, the time-varying meshing stiffness of the herringbone gear transmission system considering the root crack is calculated, and the stiffness variation law under different crack parameters is analyzed. The Runge-Kutta method is used to solve the dynamic differential equation. Combined with the overall bifurcation diagram, local time history diagram, frequency domain diagram, phase diagram and Poincaré section, the influence of different excitation frequencies and crack damage on the nonlinear dynamic characteristics of herringbone gear transmission system is analyzed.
{"title":"Nonlinear dynamic characteristics analysis of herringbone gear transmission system with tooth root crack","authors":"Shuai Mo, Dongdong Wang, Boyan Chang, Xinhao Zhao, Haruo Houjoh","doi":"10.1016/j.cnsns.2024.108572","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108572","url":null,"abstract":"Herringbone gears have been widely used in high-speed and heavy-duty fields such as ships, aerospace and automobiles due to their outstanding bearing capacity, high contact ratio, small axial force and stable transmission. Under the factors such as high speed and heavy load, the gear may crack at the root of the tooth, which affects the normal operation of the gear system. In this paper, the herringbone gear transmission system is taken as the research object, and the nonlinear dynamic model of the herringbone gear transmission system considering cracks is established under various excitation factors. According to the potential energy method, the time-varying meshing stiffness of the herringbone gear transmission system considering the root crack is calculated, and the stiffness variation law under different crack parameters is analyzed. The Runge-Kutta method is used to solve the dynamic differential equation. Combined with the overall bifurcation diagram, local time history diagram, frequency domain diagram, phase diagram and Poincaré section, the influence of different excitation frequencies and crack damage on the nonlinear dynamic characteristics of herringbone gear transmission system is analyzed.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"27 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911900","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 : 2024-12-27DOI: 10.1016/j.cnsns.2024.108562
J.D. Meiss, E. Sander
In this paper, we distinguish between four categories of dynamics for quasiperiodically-forced (QPF) circle maps: resonant and incommensurate regular dynamics, and strongly and weakly chaotic dynamics, using the weighted Birkhoff average (WBA). Regular orbits can be classified by their rotation vectors, and these can be rapidly computed to machine precision using the WBA. These orbits can be resonant or incommensurate and we distinguish between these by computing their “resonance order,” allowing us to quickly identify and observe the geometric properties of a large set of Arnold tongues. When the dynamics is chaotic the WBA converges slowly. Orbits that are not regular can be strongly chaotic, when they have a positive Lyapunov exponent, or weakly chaotic when the maximal Lyapunov exponent is not positive. The latter correspond to the strange nonchaotic attractors (SNA) that have been observed in QPF circle maps beginning with models introduced by Ding, Grebogi, and Ott. The WBA provides an efficient new technique to find SNAs, and allows us to accurately compute the proportions of each of the four orbit types as a function of map parameters.
{"title":"Resonance and weak chaos in quasiperiodically-forced circle maps","authors":"J.D. Meiss, E. Sander","doi":"10.1016/j.cnsns.2024.108562","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108562","url":null,"abstract":"In this paper, we distinguish between four categories of dynamics for quasiperiodically-forced (QPF) circle maps: resonant and incommensurate regular dynamics, and strongly and weakly chaotic dynamics, using the weighted Birkhoff average (WBA). Regular orbits can be classified by their rotation vectors, and these can be rapidly computed to machine precision using the WBA. These orbits can be resonant or incommensurate and we distinguish between these by computing their “resonance order,” allowing us to quickly identify and observe the geometric properties of a large set of Arnold tongues. When the dynamics is chaotic the WBA converges slowly. Orbits that are not regular can be <ce:italic>strongly</ce:italic> chaotic, when they have a positive Lyapunov exponent, or <ce:italic>weakly</ce:italic> chaotic when the maximal Lyapunov exponent is not positive. The latter correspond to the strange nonchaotic attractors (SNA) that have been observed in QPF circle maps beginning with models introduced by Ding, Grebogi, and Ott. The WBA provides an efficient new technique to find SNAs, and allows us to accurately compute the proportions of each of the four orbit types as a function of map parameters.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"68 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911901","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 : 2024-12-25DOI: 10.1016/j.cnsns.2024.108566
Yunru Bai, Leszek Gasiński, Nikolaos S. Papageorgiou
We consider a nonautonomous (p,q)-equation with unbalanced growth and a reaction that has the combined effects of a singular term and of a parametric superlinear perturbation which may change sign. We show that for all small values of the parameter, the problem has at least two bounded positive solutions.
{"title":"Singular double phase equations with a sign changing reaction","authors":"Yunru Bai, Leszek Gasiński, Nikolaos S. Papageorgiou","doi":"10.1016/j.cnsns.2024.108566","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108566","url":null,"abstract":"We consider a nonautonomous <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-equation with unbalanced growth and a reaction that has the combined effects of a singular term and of a parametric superlinear perturbation which may change sign. We show that for all small values of the parameter, the problem has at least two bounded positive solutions.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"38 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911905","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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