Pub Date : 2025-04-24DOI: 10.1016/j.chaos.2025.116439
Ali Moukadem , Barbara Pascal , Jean-Baptiste Courbot , Nicolas Juillet
The Stockwell Transform is a time–frequency representation resulting from an hybridization between the Short-Time Fourier Transform and the Continuous Wavelet Transform. Instead of focusing on energy maxima, an unorthodox line of research has recently shed the light on the zeros of time–frequency transforms, leading to fruitful theoretical developments combining probability theory, complex analysis and signal processing. While the distributions of zeros of the Short-Time Fourier Transform and of the Continuous Wavelet Transform of white noise have been precisely characterized, that of the Stockwell Transform of white noise zeros remains unexplored. To fill this gap, the present work proposes a characterization of the distribution of zeros of the Stockwell Transform of white noise taking advantage of a novel generalized Analytic Stockwell Transform. First of all, an analytic version of the Stockwell Transform is designed. Then, analyticity is leveraged to establish a connection with the hyperbolic Gaussian analytic function, whose zero set is invariant under the isometries of the Poincaré disk. Finally, the theoretical spatial statistics of the zeros of the hyperbolic Gaussian analytic function and the empirical statistics of the zeros the Analytic Stockwell Transform of white noise are compared through intensive Monte Carlo simulations, showing the practical relevance of the established connection. A documented Python toolbox has been made publicly available by the authors.
{"title":"The Analytic Stockwell Transform and its zeros","authors":"Ali Moukadem , Barbara Pascal , Jean-Baptiste Courbot , Nicolas Juillet","doi":"10.1016/j.chaos.2025.116439","DOIUrl":"10.1016/j.chaos.2025.116439","url":null,"abstract":"<div><div>The Stockwell Transform is a time–frequency representation resulting from an hybridization between the Short-Time Fourier Transform and the Continuous Wavelet Transform. Instead of focusing on energy maxima, an unorthodox line of research has recently shed the light on the zeros of time–frequency transforms, leading to fruitful theoretical developments combining probability theory, complex analysis and signal processing. While the distributions of zeros of the Short-Time Fourier Transform and of the Continuous Wavelet Transform of white noise have been precisely characterized, that of the Stockwell Transform of white noise zeros remains unexplored. To fill this gap, the present work proposes a characterization of the distribution of zeros of the Stockwell Transform of white noise taking advantage of a novel generalized Analytic Stockwell Transform. First of all, an analytic version of the Stockwell Transform is designed. Then, analyticity is leveraged to establish a connection with the hyperbolic Gaussian analytic function, whose zero set is invariant under the isometries of the Poincaré disk. Finally, the theoretical spatial statistics of the zeros of the hyperbolic Gaussian analytic function and the empirical statistics of the zeros the Analytic Stockwell Transform of white noise are compared through intensive Monte Carlo simulations, showing the practical relevance of the established connection. A documented Python toolbox has been made publicly available by the authors.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116439"},"PeriodicalIF":5.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863735","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 : 2025-04-24DOI: 10.1016/j.chaos.2025.116438
Jian Gao , Bin Xu , Yaqi Zheng , Chuansheng Shen
Population dynamics and reproductive cycles are fundamental aspects of biological systems, with profound implications for species survival and ecosystem stability. Synchronous reproduction, a phenomenon observed across various taxa, optimizes breeding success and offspring survival but may also introduce complex dynamics under changing environmental conditions. However, there is a scarcity of reports on the impact of synchronous reproduction on population dynamics. This study investigates the influence of synchronous reproductive cycles on population dynamics, with a focus on bifurcation phenomena such as Hopf and period-doubling bifurcations. By employing a series of ordinary differential equation (ODE) models and their discrete difference equation (DDE) counterparts, we analyze the synergistic effects of the reproductive cycle and control parameters on population stability and oscillatory behavior. Numerical simulations demonstrate that synchronous reproduction induces systematic shifts in bifurcation diagrams within the parameter space. Specifically, an increase in reproductive cycle amplifies the displacement of bifurcation curves, revealing that reproductive cycle and control parameters jointly regulate population dynamics. Our results offer actionable guidance for ecosystem management by demonstrating that maintaining or adjusting reproductive synchrony could serve as a leverage point for stabilizing vulnerable populations. Specifically, conservation strategies targeting species with synchronized breeding cycles should prioritize habitat preservation during critical reproductive windows and incorporate climate-driven shifts in reproductive timing into adaptive management frameworks.
{"title":"Population dynamics of biological synchronous reproduction and the effects of synchronous reproductive cycle on population dynamics","authors":"Jian Gao , Bin Xu , Yaqi Zheng , Chuansheng Shen","doi":"10.1016/j.chaos.2025.116438","DOIUrl":"10.1016/j.chaos.2025.116438","url":null,"abstract":"<div><div>Population dynamics and reproductive cycles are fundamental aspects of biological systems, with profound implications for species survival and ecosystem stability. Synchronous reproduction, a phenomenon observed across various taxa, optimizes breeding success and offspring survival but may also introduce complex dynamics under changing environmental conditions. However, there is a scarcity of reports on the impact of synchronous reproduction on population dynamics. This study investigates the influence of synchronous reproductive cycles on population dynamics, with a focus on bifurcation phenomena such as Hopf and period-doubling bifurcations. By employing a series of ordinary differential equation (ODE) models and their discrete difference equation (DDE) counterparts, we analyze the synergistic effects of the reproductive cycle and control parameters on population stability and oscillatory behavior. Numerical simulations demonstrate that synchronous reproduction induces systematic shifts in bifurcation diagrams within the parameter space. Specifically, an increase in reproductive cycle amplifies the displacement of bifurcation curves, revealing that reproductive cycle and control parameters jointly regulate population dynamics. Our results offer actionable guidance for ecosystem management by demonstrating that maintaining or adjusting reproductive synchrony could serve as a leverage point for stabilizing vulnerable populations. Specifically, conservation strategies targeting species with synchronized breeding cycles should prioritize habitat preservation during critical reproductive windows and incorporate climate-driven shifts in reproductive timing into adaptive management frameworks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116438"},"PeriodicalIF":5.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863736","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 : 2025-04-24DOI: 10.1016/j.chaos.2025.116441
S. Sanjay , S. Saravana Veni , Boris A. Malomed
In the context of the mean-field exciton-polariton (EP) theory with balanced loss and pump, we investigate the formation of lattice structures built of individual vortex-antivortex (VAV) bound states under the action of the two-dimensional harmonic-oscillator (HO) potential trap and effective spin–orbit coupling (SOC), produced by the TE-TM splitting in the polariton system. The number of VAV elements (“pixels”) building the structures grow with the increase of self- and cross-interaction coefficients. Depending upon their values and the trapping frequency, stable ring-shaped, circular, square-shaped, rectangular, pentagonal, hexagonal, and triangular patterns are produced, with the central site left vacant or occupied in the lattice patterns of different types. The results suggest the experimental creation of the new patterns and their possible use for the design of integrated circuits in EP setups, controlled by the strengths of the TE-TM splitting, nonlinearity, and HO trap.
{"title":"Vortex droplets and lattice patterns in two-dimensional traps: A photonic spin–orbit-coupling perspective","authors":"S. Sanjay , S. Saravana Veni , Boris A. Malomed","doi":"10.1016/j.chaos.2025.116441","DOIUrl":"10.1016/j.chaos.2025.116441","url":null,"abstract":"<div><div>In the context of the mean-field exciton-polariton (EP) theory with balanced loss and pump, we investigate the formation of lattice structures built of individual vortex-antivortex (VAV) bound states under the action of the two-dimensional harmonic-oscillator (HO) potential trap and effective spin–orbit coupling (SOC), produced by the TE-TM splitting in the polariton system. The number of VAV elements (“pixels”) building the structures grow with the increase of self- and cross-interaction coefficients. Depending upon their values and the trapping frequency, stable ring-shaped, circular, square-shaped, rectangular, pentagonal, hexagonal, and triangular patterns are produced, with the central site left vacant or occupied in the lattice patterns of different types. The results suggest the experimental creation of the new patterns and their possible use for the design of integrated circuits in EP setups, controlled by the strengths of the TE-TM splitting, nonlinearity, and HO trap.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116441"},"PeriodicalIF":5.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863737","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 : 2025-04-23DOI: 10.1016/j.chaos.2025.116434
Chandra S. Pappu , Aubrey N. Beal , Jonathan N. Blakely , Ned J. Corron
We present the correlation properties and ambiguity surfaces for a first-order, nonautonomous, chaotic oscillator with a closed-form analytic solution. Unlike most chaotic systems, the solutions of this oscillator take the form of a linear superposition of fixed basis functions weighted by a phase-coded symbol sequence. These solutions enable the analytic investigation of important receiver metrics of systems in a manner that is seldom available when considering chaotic systems. These new, low-order systems exhibit less structure in their basis functions and produce favorable correlation properties with significant mainlobe peak and sidelobe levels below to . Further, averaged ambiguity function results show a ‘thumbtack’ profile with a low-variance, single, localized peak. Consequently, our work validates the ability of these waveforms to resolve multiple-point targets on range-Doppler planes. These desirable characteristics indicate that nonautonomous solvable chaos has significant potential in supporting novel radar, sonar, and remote sensing technologies.
{"title":"Analytic range-Doppler ambiguities for nonautonomous solvable chaos","authors":"Chandra S. Pappu , Aubrey N. Beal , Jonathan N. Blakely , Ned J. Corron","doi":"10.1016/j.chaos.2025.116434","DOIUrl":"10.1016/j.chaos.2025.116434","url":null,"abstract":"<div><div>We present the correlation properties and ambiguity surfaces for a first-order, nonautonomous, chaotic oscillator with a closed-form analytic solution. Unlike most chaotic systems, the solutions of this oscillator take the form of a linear superposition of fixed basis functions weighted by a phase-coded symbol sequence. These solutions enable the analytic investigation of important receiver metrics of systems in a manner that is seldom available when considering chaotic systems. These new, low-order systems exhibit less structure in their basis functions and produce favorable correlation properties with significant mainlobe peak and sidelobe levels below <span><math><mrow><mo>−</mo><mn>20</mn><mspace></mspace><mi>d</mi><mi>B</mi></mrow></math></span> to <span><math><mrow><mo>−</mo><mn>30</mn><mspace></mspace><mi>d</mi><mi>B</mi></mrow></math></span>. Further, averaged ambiguity function results show a ‘thumbtack’ profile with a low-variance, single, localized peak. Consequently, our work validates the ability of these waveforms to resolve multiple-point targets on range-Doppler planes. These desirable characteristics indicate that nonautonomous solvable chaos has significant potential in supporting novel radar, sonar, and remote sensing technologies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116434"},"PeriodicalIF":5.3,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863734","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 : 2025-04-23DOI: 10.1016/j.chaos.2025.116419
Z. Navickas , R. Marcinkevicius , I. Telksniene , T. Telksnys , R. Mickevicius , M. Ragulskis
The concept of the deformed solitary solutions is introduced in this paper. It is demonstrated that deformed solitary solutions to nonlinear differential equations can exist even if those equations do not admit classical solitary solutions. The proposed technique for the derivation of deformed solitary solutions does yield not only the analytical closed-form structure of the solution, but also automatically derives the conditions for its existence in the space of system parameters. Analytical and computational techniques are used to derive and to illustrate deformed kink solitary solutions to the mathematical model for tumor–immune system interactions.
{"title":"Beyond solitons: Deformed solitary solutions to the mathematical model of tumor–immune system interactions","authors":"Z. Navickas , R. Marcinkevicius , I. Telksniene , T. Telksnys , R. Mickevicius , M. Ragulskis","doi":"10.1016/j.chaos.2025.116419","DOIUrl":"10.1016/j.chaos.2025.116419","url":null,"abstract":"<div><div>The concept of the deformed solitary solutions is introduced in this paper. It is demonstrated that deformed solitary solutions to nonlinear differential equations can exist even if those equations do not admit classical solitary solutions. The proposed technique for the derivation of deformed solitary solutions does yield not only the analytical closed-form structure of the solution, but also automatically derives the conditions for its existence in the space of system parameters. Analytical and computational techniques are used to derive and to illustrate deformed kink solitary solutions to the mathematical model for tumor–immune system interactions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116419"},"PeriodicalIF":5.3,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860645","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 : 2025-04-23DOI: 10.1016/j.chaos.2025.116437
Ertong Wang , Bin Hu , Zhi-Hong Guan
The influence of neural synapses on the collaboration of different brain regions is an urgent need for current research. In this paper, a multi-region neural network (MRNN) is proposed using multistable locally-active memristor (MLAM). A new memristor is first designed with multistable, non-volatile, and locally-active. Then, the memristor is modeled as a neural synapse connecting two different regions to construct the MRNN, which is a multistable locally-active memristive Hopfield neural network. The neural network exhibits rich chaotic dynamics, and the dynamic coupling strength of the synapse is analyzed using bifurcation, phase diagrams, and two-parameter chaotic maps. The neural network also demonstrates self-boosting of attractors driven by the parameters of synapse. The effect of memristive parameters on the self-boosting of the attractor is revealed by describing the phase diagram and the basin of attraction. In order to explore the collective behavior of the proposed network, controllers are further designed to realize the state synchronization cross multiple brain regions.
{"title":"Chaotic dynamics and synchronization of multi-region neural network based on locally active memristor","authors":"Ertong Wang , Bin Hu , Zhi-Hong Guan","doi":"10.1016/j.chaos.2025.116437","DOIUrl":"10.1016/j.chaos.2025.116437","url":null,"abstract":"<div><div>The influence of neural synapses on the collaboration of different brain regions is an urgent need for current research. In this paper, a multi-region neural network (MRNN) is proposed using multistable locally-active memristor (MLAM). A new memristor is first designed with multistable, non-volatile, and locally-active. Then, the memristor is modeled as a neural synapse connecting two different regions to construct the MRNN, which is a multistable locally-active memristive Hopfield neural network. The neural network exhibits rich chaotic dynamics, and the dynamic coupling strength of the synapse is analyzed using bifurcation, phase diagrams, and two-parameter chaotic maps. The neural network also demonstrates self-boosting of attractors driven by the parameters of synapse. The effect of memristive parameters on the self-boosting of the attractor is revealed by describing the phase diagram and the basin of attraction. In order to explore the collective behavior of the proposed network, controllers are further designed to realize the state synchronization cross multiple brain regions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116437"},"PeriodicalIF":5.3,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860646","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 : 2025-04-23DOI: 10.1016/j.chaos.2025.116435
Xiaoyang Wang , Qidong Fu , Changming Huang
In this study, we investigate the optical properties of linear and nonlinear topological in-phase, out-of-phase, and edge modes in a defected dimer lattice with fourth-order diffraction, encompassing their bifurcation characteristics, localized field distributions, and stability properties. Both focusing and defocusing nonlinearities are considered. Within the nontrivial regime, in-phase, out-of-phase, and edge modes can emerge within the gap. Numerical results reveal that three types of topological gap solitons bifurcate from their corresponding linear localized modes. The dimerization parameter can be tuned to drive the system from a trivial to a nontrivial configuration. We observe that as the strength of the fourth-order diffraction increases, the size of the spectral gap also enlarges, with this parameter effectively broadening the stability window for solitons. Our findings offer novel insights into the properties of both linear and nonlinear modes in topologically defected structures.
{"title":"Topological linear and nonlinear gap modes in defected dimer lattice with fourth-order diffraction","authors":"Xiaoyang Wang , Qidong Fu , Changming Huang","doi":"10.1016/j.chaos.2025.116435","DOIUrl":"10.1016/j.chaos.2025.116435","url":null,"abstract":"<div><div>In this study, we investigate the optical properties of linear and nonlinear topological in-phase, out-of-phase, and edge modes in a defected dimer lattice with fourth-order diffraction, encompassing their bifurcation characteristics, localized field distributions, and stability properties. Both focusing and defocusing nonlinearities are considered. Within the nontrivial regime, in-phase, out-of-phase, and edge modes can emerge within the gap. Numerical results reveal that three types of topological gap solitons bifurcate from their corresponding linear localized modes. The dimerization parameter can be tuned to drive the system from a trivial to a nontrivial configuration. We observe that as the strength of the fourth-order diffraction increases, the size of the spectral gap also enlarges, with this parameter effectively broadening the stability window for solitons. Our findings offer novel insights into the properties of both linear and nonlinear modes in topologically defected structures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116435"},"PeriodicalIF":5.3,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860647","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 : 2025-04-19DOI: 10.1016/j.chaos.2025.116436
Joseph Páez Chávez , Aytül Gökçe , Thomas Götz , Burcu Gürbüz
In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over time. The SIRSV-model divides the population into four compartments and introduces periodic re-vaccination for waning immunity. The efficacy of the vaccine is assumed to decay with the time passed since the vaccination. Periodic re-vaccinations are applied to the population. We develop a partial differential equation (PDE) model for the continuous vaccination time and a coupled ordinary differential equation (ODE) system when discretizing the vaccination period. We analyze the equilibria of the ODE model and investigate the linear stability of the disease-free equilibrium (DFE). Furthermore, we explore an optimization framework where vaccination rate, re-vaccination time, and non-pharmaceutical interventions (NPIs) are control variables to minimize infection levels. The optimization objective is defined using different norm-based measures of infected individuals. A numerical analysis of the model’s dynamic behavior under varying control parameters is conducted using path-following methods. The analysis focuses on the impacts of vaccination strategies and contact limitation measures. Bifurcation analysis reveals complex behaviors, including bistability, fold bifurcations, forward and backward bifurcations, highlighting the need for combined vaccination and contact control strategies to manage disease spread effectively.
{"title":"An SIRS-model considering waning efficacy and periodic re-vaccination","authors":"Joseph Páez Chávez , Aytül Gökçe , Thomas Götz , Burcu Gürbüz","doi":"10.1016/j.chaos.2025.116436","DOIUrl":"10.1016/j.chaos.2025.116436","url":null,"abstract":"<div><div>In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over time. The SIRSV-model divides the population into four compartments and introduces periodic re-vaccination for waning immunity. The efficacy of the vaccine is assumed to decay with the time passed since the vaccination. Periodic re-vaccinations are applied to the population. We develop a partial differential equation (PDE) model for the continuous vaccination time and a coupled ordinary differential equation (ODE) system when discretizing the vaccination period. We analyze the equilibria of the ODE model and investigate the linear stability of the disease-free equilibrium (DFE). Furthermore, we explore an optimization framework where vaccination rate, re-vaccination time, and non-pharmaceutical interventions (NPIs) are control variables to minimize infection levels. The optimization objective is defined using different norm-based measures of infected individuals. A numerical analysis of the model’s dynamic behavior under varying control parameters is conducted using path-following methods. The analysis focuses on the impacts of vaccination strategies and contact limitation measures. Bifurcation analysis reveals complex behaviors, including bistability, fold bifurcations, forward and backward bifurcations, highlighting the need for combined vaccination and contact control strategies to manage disease spread effectively.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116436"},"PeriodicalIF":5.3,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848329","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 : 2025-04-19DOI: 10.1016/j.chaos.2025.116407
Xu Zhao , Yang Gao , Haisong Huang , Qingsong Fan , Jiajia Chen , Muhammet Deveci , Weiping Ding
This paper develops an adaptive neural finite-time tracking control scheme based on modified command-filtered backstepping control method (MCFBC) for multi-input and multi-output (MIMO) nonlinear systems. Firstly, by introducing some constant matrices, command-filtered backstepping control method (CFBC) is modified. Compared with CFBC, MCFBC ensures that virtual control signals are linearized, which lowers the complexity of the controller such that the control performance is elevated. Secondly, different from CFBC, MCFBC does not directly use the spectral boundedness of control directions in stability proof any more. Thirdly, lumped uncertainties are approximated by neural network (NN) and a more generalized inequality is proposed to surmount the technical difficulties of finite-time stability analysis. Fourthly, the singularity problem is circumvented. Command filters are introduced to remove the repeated differentiation of pseudocontrol signals. An error compensation system is constructed to lower the adverse effect from filter errors. This proposed controller guarantees that all signals in the closed-loop system converge to a bounded region within finite time and the system output can follow the given signal with a considerably small tracking error. Finally, flexible joint manipulations are used to validate this control scheme.
{"title":"Adaptive neural finite-time tracking control based on modified command-filtered backstepping method for MIMO nonlinear systems","authors":"Xu Zhao , Yang Gao , Haisong Huang , Qingsong Fan , Jiajia Chen , Muhammet Deveci , Weiping Ding","doi":"10.1016/j.chaos.2025.116407","DOIUrl":"10.1016/j.chaos.2025.116407","url":null,"abstract":"<div><div>This paper develops an adaptive neural finite-time tracking control scheme based on modified command-filtered backstepping control method (MCFBC) for multi-input and multi-output (MIMO) nonlinear systems. Firstly, by introducing some constant matrices, command-filtered backstepping control method (CFBC) is modified. Compared with CFBC, MCFBC ensures that virtual control signals are linearized, which lowers the complexity of the controller such that the control performance is elevated. Secondly, different from CFBC, MCFBC does not directly use the spectral boundedness of control directions in stability proof any more. Thirdly, lumped uncertainties are approximated by neural network (NN) and a more generalized inequality is proposed to surmount the technical difficulties of finite-time stability analysis. Fourthly, the singularity problem is circumvented. Command filters are introduced to remove the repeated differentiation of pseudocontrol signals. An error compensation system is constructed to lower the adverse effect from filter errors. This proposed controller guarantees that all signals in the closed-loop system converge to a bounded region within finite time and the system output can follow the given signal with a considerably small tracking error. Finally, flexible joint manipulations are used to validate this control scheme.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116407"},"PeriodicalIF":5.3,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848330","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 : 2025-04-19DOI: 10.1016/j.chaos.2025.116448
Jian Wang , Maddina Dinesh Kumar , S.U. Mamatha , Thandra Jithendra , Marouan Kouki , Nehad Ali Shah
This work investigates the new and complete characteristics of radiation, magnetic field, and heat source/sink in the unstable thin-film flow of ternary and hybrid nanofluids over the stretching surface with oscillatory boundary conditions. of radiation, magnetic field, and heat source/sink in the unstable thin-film flow of ternary and hybrid nanofluids over the stretching surface with oscillatory boundary conditions. The flow field is mathematically formulated and solved numerically using BVP5C and deep neural networks with MATLAB software; considering industrial applications, Ethylene glycol (EG) is taken as base fluid, and the nanoparticles utilised in this study include Aluminium oxide , carbon nanotubes with one or more walls (SWCNTs, MWCNTs). Further, the model is trained by adapting the deep neural network (DNN) technique. Graphical simulations are prepared for Case 1: and Case 2: . To analyse the significance of unsteadiness, Prandtl, Eckert number, radiation, magnetic, film thickness, source/sink parameter on velocity, temperature and Nusselt number. The research showcases that heat transfer is high in compared with hybrid nanofluid. Increasing the layer thickness and unsteadiness parameters lowers temperature and velocity. Applied DNN model shown to be extremely useful for prediction and estimation. Obtained results are helpful in the formulation of advanced products and processes.
{"title":"Deep learning-based Adam optimization for magnetohydrodynamics radiative thin film flow of ternary hybrid nanofluid with oscillatory boundary conditions","authors":"Jian Wang , Maddina Dinesh Kumar , S.U. Mamatha , Thandra Jithendra , Marouan Kouki , Nehad Ali Shah","doi":"10.1016/j.chaos.2025.116448","DOIUrl":"10.1016/j.chaos.2025.116448","url":null,"abstract":"<div><div>This work investigates the new and complete characteristics of radiation, magnetic field, and heat source/sink in the unstable thin-film flow of ternary and hybrid nanofluids over the stretching surface with oscillatory boundary conditions. of radiation, magnetic field, and heat source/sink in the unstable thin-film flow of ternary and hybrid nanofluids over the stretching surface with oscillatory boundary conditions. The flow field is mathematically formulated and solved numerically using BVP5C and deep neural networks with MATLAB software; considering industrial applications, Ethylene glycol (EG) is taken as base fluid, and the nanoparticles utilised in this study include Aluminium oxide <span><math><mfenced><mrow><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></mrow></mfenced></math></span>, carbon nanotubes with one or more walls (SWCNTs, MWCNTs). Further, the model is trained by adapting the deep neural network (DNN) technique. Graphical simulations are prepared for Case 1: <span><math><mi>EG</mi><mo>+</mo><mtext>SWCNT</mtext><mo>+</mo><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></math></span> and Case 2: <span><math><mi>EG</mi><mo>+</mo><mtext>SWCNT</mtext><mo>+</mo><mtext>MWCNT</mtext><mo>+</mo><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></math></span>. To analyse the significance of unsteadiness, Prandtl, Eckert number, radiation, magnetic, film thickness, source/sink parameter on velocity, temperature and Nusselt number. The research showcases that heat transfer is high in <span><math><mi>EG</mi><mo>+</mo><mtext>SWCNT</mtext><mo>+</mo><mtext>MWCNT</mtext><mo>+</mo><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></math></span> compared with <span><math><mi>EG</mi><mo>+</mo><mtext>SWCNT</mtext><mo>+</mo><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub></math></span> hybrid nanofluid. Increasing the layer thickness and unsteadiness parameters lowers temperature and velocity. Applied DNN model shown to be extremely useful for prediction and estimation. Obtained results are helpful in the formulation of advanced products and processes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116448"},"PeriodicalIF":5.3,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848331","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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