Pub Date : 2026-01-15DOI: 10.1016/j.cnsns.2026.109756
T. Akinaga , P.M.J. Trevelyan , S.C. Generalis
We consider a vertical rectangular tube of large aspect ratio with side-wall heating in order to mimic realistic experimental conditions. We therefore impose the condition that across any lateral cross-section of the rectangular tube the fluid flow vanishes. We find through our numerical analysis that oscillatory modes yield critical conditions and offer therefore sequential bifurcations that lead to the turbulent regime. Although the linear stability analysis is the same as the case where the imposed constant flux condition is absent, the corresponding nonlinear regime displays fundamentally different characteristics to the open narrow channel case. Here we focus on the sequence of bifurcations approach of a fluid enclosed in a rectangular tube, aligning with engineering applications. We additionally assume the limit of small Prandtl number and thus the effects caused by temperature perturbations are negligible. Finally we identify the oscillatory states that lead to turbulence as the Grashof number increases up to the value 1000. Our fully nonlinear numerical analysis shows that all bifurcations are supercritical and here we concentrate on the critical axial wavenumber of the linear stability analysis of the laminar flow and its pairing with a specific azimuthal wavenumber.
{"title":"Tertiary, quaternary and higher order states in the sequence of bifurcations approach (SBA) to turbulence for laterally heated shear flows within a rectangular tube","authors":"T. Akinaga , P.M.J. Trevelyan , S.C. Generalis","doi":"10.1016/j.cnsns.2026.109756","DOIUrl":"10.1016/j.cnsns.2026.109756","url":null,"abstract":"<div><div>We consider a vertical rectangular tube of large aspect ratio with side-wall heating in order to mimic realistic experimental conditions. We therefore impose the condition that across any lateral cross-section of the rectangular tube the fluid flow vanishes. We find through our numerical analysis that oscillatory modes yield critical conditions and offer therefore sequential bifurcations that lead to the turbulent regime. Although the linear stability analysis is the same as the case where the imposed constant flux condition is absent, the corresponding nonlinear regime displays fundamentally different characteristics to the open narrow channel case. Here we focus on the sequence of bifurcations approach of a fluid enclosed in a rectangular tube, aligning with engineering applications. We additionally assume the limit of small Prandtl number and thus the effects caused by temperature perturbations are negligible. Finally we identify the oscillatory states that lead to turbulence as the Grashof number increases up to the value 1000. Our fully nonlinear numerical analysis shows that all bifurcations are supercritical and here we concentrate on the critical axial wavenumber of the linear stability analysis of the laminar flow and its pairing with a specific azimuthal wavenumber.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109756"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995145","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 : 2026-01-15DOI: 10.1016/j.cnsns.2026.109682
Yufei Ye , Wen Qin , Mouquan Shen , Zhihao Zhang , Hany M. Hasanien , Zheng H. Zhu
This paper is devoted to fixed-time synchronization for a class of heterogeneous complex networks. A composite controller is developed by two main parts, namely, a hyperbolic sine functions instead of summation of two power functions is adopted to supply a smaller fixed time and less design parameters and a compensation term is utilized to deal with the network node heterogeneity. Resorting impulsive interval partitioning and convex combination, a sufficient condition expressed by matrix inequalities is established to guarantee fixed-time synchronization of the resultant systems. A numerical simulation is employed to validate the efficiency of the proposed fixed-time synchronization control scheme.
{"title":"Fixed-time impulsive synchronization of heterogeneous complex networks","authors":"Yufei Ye , Wen Qin , Mouquan Shen , Zhihao Zhang , Hany M. Hasanien , Zheng H. Zhu","doi":"10.1016/j.cnsns.2026.109682","DOIUrl":"10.1016/j.cnsns.2026.109682","url":null,"abstract":"<div><div>This paper is devoted to fixed-time synchronization for a class of heterogeneous complex networks. A composite controller is developed by two main parts, namely, a hyperbolic sine functions instead of summation of two power functions is adopted to supply a smaller fixed time and less design parameters and a compensation term is utilized to deal with the network node heterogeneity. Resorting impulsive interval partitioning and convex combination, a sufficient condition expressed by matrix inequalities is established to guarantee fixed-time synchronization of the resultant systems. A numerical simulation is employed to validate the efficiency of the proposed fixed-time synchronization control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109682"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995141","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 : 2026-01-15DOI: 10.1016/j.cnsns.2026.109681
Yonghong Yao , Sani Salisu , Yekini Shehu
This paper introduces a relaxed version of the forward-backward-forward algorithm with extrapolation from the past iterates to solve variational inequality problems in Hilbert spaces. The relaxation parameter is added to the proposed algorithm to reduce oscillations, providing robustness to a poor choice of initial guess during implementations. Some recently proposed forward-backward-forward algorithms with extrapolation from the past are recovered from our algorithm. We establish that the sequence of iterates generated by our algorithm weakly converges to a solution of the variational inequality problem guided by a pseudo-monotone and Lipschitz continuous operator. We also provide the error bounds of the algorithm in terms of the gap function for the ergodic iterates, which have a convergence rate of . Numerical results are given from optimal control and image restoration problems.
{"title":"Solving variational inequalities using an algorithm with extrapolations from the past and relaxation","authors":"Yonghong Yao , Sani Salisu , Yekini Shehu","doi":"10.1016/j.cnsns.2026.109681","DOIUrl":"10.1016/j.cnsns.2026.109681","url":null,"abstract":"<div><div>This paper introduces a relaxed version of the forward-backward-forward algorithm with extrapolation from the past iterates to solve variational inequality problems in Hilbert spaces. The relaxation parameter is added to the proposed algorithm to reduce oscillations, providing robustness to a poor choice of initial guess during implementations. Some recently proposed forward-backward-forward algorithms with extrapolation from the past are recovered from our algorithm. We establish that the sequence of iterates generated by our algorithm weakly converges to a solution of the variational inequality problem guided by a pseudo-monotone and Lipschitz continuous operator. We also provide the error bounds of the algorithm in terms of the gap function for the ergodic iterates, which have a convergence rate of <span><math><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><mi>n</mi><mo>)</mo></mrow></math></span>. Numerical results are given from optimal control and image restoration problems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109681"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995144","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 : 2026-01-15DOI: 10.1016/j.cnsns.2026.109703
Pengfei Guo , Yunong Zhang , Zheng-an Yao , Shuai Li
Temporally dependent generalized Sylvester’s matrix equation (TDGSME), a type of temporally dependent linear matrix problem, plays essential roles in intelligent science and engineering fields due to the explosion of data streams and the requirements of online computing. Zhang neural network (ZNN), first developed by Zhang et al. in 2001, has been efficiently adopted to tackle numerous specialized situations of TDGSME problems. However, previous studies on TDGSME mainly focused on the natural exponential convergence property of the ZNN model. In this paper, based on temporally dependent nonlinear systems control theory, we consider the original ZNN model for solving the TDGSME problem by discussing its inherent properties, including nearly fixed-time convergence, error feedback-related noise tolerance, infinite interval continuity, and overall significance. Additionally, we propose the left-right four-step rule ZNN (LRFSR-ZNN) algorithm to address the future generalized Sylvester’s matrix equation (FGSME) problem. Moreover, using Lyapunov stability theory, comparative methods of nonlinear perturbed systems, and convex optimization theory, we rigorously prove these inherent properties of the original ZNN model for tackling the TDGSME problem. Furthermore, we conduct four numerical experiments, including temporally dependent Lyapunov matrix equation, temporally dependent Sylvester’s matrix equation, temporally dependent Stein’s matrix equation, and temporally dependent Kalman-Yakubovich matrix equation, to verify the theoretical results of the inherent properties of the ZNN model. Additionally, we employ the LRFSR-ZNN algorithm to conduct two simulations for tackling the motion planning problem of robot manipulators, and the simulation results confirm the superiority and robustness of our proposed algorithm.
{"title":"Zhang neural network model and algorithm with inherent properties for tackling temporally dependent generalized Sylvester’s matrix equation problems with applications","authors":"Pengfei Guo , Yunong Zhang , Zheng-an Yao , Shuai Li","doi":"10.1016/j.cnsns.2026.109703","DOIUrl":"10.1016/j.cnsns.2026.109703","url":null,"abstract":"<div><div>Temporally dependent generalized Sylvester’s matrix equation (TDGSME), a type of temporally dependent linear matrix problem, plays essential roles in intelligent science and engineering fields due to the explosion of data streams and the requirements of online computing. Zhang neural network (ZNN), first developed by Zhang et al. in 2001, has been efficiently adopted to tackle numerous specialized situations of TDGSME problems. However, previous studies on TDGSME mainly focused on the natural exponential convergence property of the ZNN model. In this paper, based on temporally dependent nonlinear systems control theory, we consider the original ZNN model for solving the TDGSME problem by discussing its inherent properties, including nearly fixed-time convergence, error feedback-related noise tolerance, infinite interval continuity, and overall significance. Additionally, we propose the left-right four-step rule ZNN (LRFSR-ZNN) algorithm to address the future generalized Sylvester’s matrix equation (FGSME) problem. Moreover, using Lyapunov stability theory, comparative methods of nonlinear perturbed systems, and convex optimization theory, we rigorously prove these inherent properties of the original ZNN model for tackling the TDGSME problem. Furthermore, we conduct four numerical experiments, including temporally dependent Lyapunov matrix equation, temporally dependent Sylvester’s matrix equation, temporally dependent Stein’s matrix equation, and temporally dependent Kalman-Yakubovich matrix equation, to verify the theoretical results of the inherent properties of the ZNN model. Additionally, we employ the LRFSR-ZNN algorithm to conduct two simulations for tackling the motion planning problem of robot manipulators, and the simulation results confirm the superiority and robustness of our proposed algorithm.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109703"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995138","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 : 2026-01-15DOI: 10.1016/j.cnsns.2026.109730
Huihui Song , Zezhou Fan , Yitong Liu , Xin Zhang
This paper investigates the inner synchronized stationary distribution of delayed signed networks with Markovian switching (DMSNs) by investigating convergence and uniform boundedness of the solution of the error system. The Lyapunov method and the signed digraph theory are applied to investigating the existence of stationary distribution, which avoids the difficulty of constructing the Lyapunov function construction directly. Then two synchronized stationary distribution criteria which ensure DMSNs exist stationary distribution are presented. Finally, the proposed theoretical results are applied to Chua’s circuit, and through corresponding numerical simulations, the validity of the theoretical results is verified.
{"title":"Synchronized stationary distribution of Markovian switching stochastic delayed signed networks with application to Chua’s circuits","authors":"Huihui Song , Zezhou Fan , Yitong Liu , Xin Zhang","doi":"10.1016/j.cnsns.2026.109730","DOIUrl":"10.1016/j.cnsns.2026.109730","url":null,"abstract":"<div><div>This paper investigates the inner synchronized stationary distribution of delayed signed networks with Markovian switching (DMSNs) by investigating convergence and uniform boundedness of the solution of the error system. The Lyapunov method and the signed digraph theory are applied to investigating the existence of stationary distribution, which avoids the difficulty of constructing the Lyapunov function construction directly. Then two synchronized stationary distribution criteria which ensure DMSNs exist stationary distribution are presented. Finally, the proposed theoretical results are applied to Chua’s circuit, and through corresponding numerical simulations, the validity of the theoretical results is verified.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109730"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145982094","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 : 2026-01-14DOI: 10.1016/j.cnsns.2026.109699
P. Sozhaeswari , Y. Lim , T. Satheesh , Sultan Alfarhood , Mejdl Safran , R. Sakthivel
The objective of this study is to address the finite-time stabilization problem for mode-dependent partial differential equation systems governed by the parabolic model with parameter uncertainties and external disturbances under a reliable boundary control protocol. Specifically, the approach of finite-time boundedness and input-output finite-time stability are deployed in tandem to limit both state and output, respectively, during certain transients. Moreover, to enhance the system’s operational effectiveness and reduce the cost function, a particle swarm optimization algorithm is employed. Furthermore, a mode-dependent proportional-integral observer is put forth to estimate the states of a mode-dependent parabolic partial differential equation systems. Thereafter, reliable boundary control is developed to attain the intended outcomes. Specifically in the design of control, the faulty actuator model which includes both linear and nonlinear aspects, are considered, to enhance the robustness of the controller. Subsequently, through the implementation of the mode-dependent Lyapunov functions and the integral-based Wirtinger’s inequality, the requisite criteria are established within the framework of linear matrix inequalities to ascertain both input-output finite-time stabilization and finite-time boundedness of the assessed system. Simultaneously, the established criteria facilitate the determination of both the developed controller and the proportional-integral observer gain matrices. Eventually, two numerical examples are provided to validate the effectiveness and applicability of the devised control protocol.
{"title":"Design of optimization-based reliable boundary control for mode-dependent parabolic PDE systems","authors":"P. Sozhaeswari , Y. Lim , T. Satheesh , Sultan Alfarhood , Mejdl Safran , R. Sakthivel","doi":"10.1016/j.cnsns.2026.109699","DOIUrl":"10.1016/j.cnsns.2026.109699","url":null,"abstract":"<div><div>The objective of this study is to address the finite-time stabilization problem for mode-dependent partial differential equation systems governed by the parabolic model with parameter uncertainties and external disturbances under a reliable boundary control protocol. Specifically, the approach of finite-time boundedness and input-output finite-time stability are deployed in tandem to limit both state and output, respectively, during certain transients. Moreover, to enhance the system’s operational effectiveness and reduce the cost function, a particle swarm optimization algorithm is employed. Furthermore, a mode-dependent proportional-integral observer is put forth to estimate the states of a mode-dependent parabolic partial differential equation systems. Thereafter, reliable boundary control is developed to attain the intended outcomes. Specifically in the design of control, the faulty actuator model which includes both linear and nonlinear aspects, are considered, to enhance the robustness of the controller. Subsequently, through the implementation of the mode-dependent Lyapunov functions and the integral-based Wirtinger’s inequality, the requisite criteria are established within the framework of linear matrix inequalities to ascertain both input-output finite-time stabilization and finite-time boundedness of the assessed system. Simultaneously, the established criteria facilitate the determination of both the developed controller and the proportional-integral observer gain matrices. Eventually, two numerical examples are provided to validate the effectiveness and applicability of the devised control protocol.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109699"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995150","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 : 2026-01-14DOI: 10.1016/j.cnsns.2026.109708
Aurélien Grolet , Cyril Touzé , André De Figueiredo Stabile , Olivier Thomas
This paper introduces a model-order reduction technique for lightly damped nonlinear vibrating systems. By combining calculation details that are specific to the harmonic balance method, the asymptotic numerical method, and the normal form style parametrisation for invariant manifolds, a complete procedure that can cope with single-mode reduction is detailed. Introducing harmonic decomposition in the process allows for a different treatment of the temporal information of the solution, which comes with advantages as compared to normal form expansions based on polynomial expansions. The computation proceeds with two nested loops on both the harmonics and the polynomial degree expansion. A decisive advantage of the procedure is its ability to compute a new expansion from a known solution, which allows the derivation of amplitude-dependent piecewise reduced order models (ROMs), together with an integrated procedure that can switch from the invariant manifolds computation attached to either fixed points or limit cycles. Once the validity limit of a first expansion is met, the procedure can restart from a point where convergence is reached and produce a new ROM. This feature has the potential to overcome the well-known limitations of asymptotic expansions associated with the parametrisation method for invariant manifolds, and is derived here only for conservative systems. The whole analysis also clearly establishes the links existing between the normal form approach and computations based on the harmonic balance combined with the asymptotic numerical method. Examples of increasing complexity, starting from a Duffing equation, a two-degree-of-freedom system and a finite element beam model, are analysed, and comparisons with existing techniques are provided.
{"title":"A harmonic balance normal form parametrisation for single mode reduction of nonlinear vibrating systems","authors":"Aurélien Grolet , Cyril Touzé , André De Figueiredo Stabile , Olivier Thomas","doi":"10.1016/j.cnsns.2026.109708","DOIUrl":"10.1016/j.cnsns.2026.109708","url":null,"abstract":"<div><div>This paper introduces a model-order reduction technique for lightly damped nonlinear vibrating systems. By combining calculation details that are specific to the harmonic balance method, the asymptotic numerical method, and the normal form style parametrisation for invariant manifolds, a complete procedure that can cope with single-mode reduction is detailed. Introducing harmonic decomposition in the process allows for a different treatment of the temporal information of the solution, which comes with advantages as compared to normal form expansions based on polynomial expansions. The computation proceeds with two nested loops on both the harmonics and the polynomial degree expansion. A decisive advantage of the procedure is its ability to compute a new expansion from a known solution, which allows the derivation of amplitude-dependent piecewise reduced order models (ROMs), together with an integrated procedure that can switch from the invariant manifolds computation attached to either fixed points or limit cycles. Once the validity limit of a first expansion is met, the procedure can restart from a point where convergence is reached and produce a new ROM. This feature has the potential to overcome the well-known limitations of asymptotic expansions associated with the parametrisation method for invariant manifolds, and is derived here only for conservative systems. The whole analysis also clearly establishes the links existing between the normal form approach and computations based on the harmonic balance combined with the asymptotic numerical method. Examples of increasing complexity, starting from a Duffing equation, a two-degree-of-freedom system and a finite element beam model, are analysed, and comparisons with existing techniques are provided.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109708"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995147","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 : 2026-01-14DOI: 10.1016/j.cnsns.2026.109664
Zenghui Hu , Jiamin Liu , Yiming Wang , Lijie You
The almost surely exponential stability (ES a.s.) is investigated for nonlinear systems subject to the effects of stochastic noises and random impulses. The randomness of impulsive effects is considered in two aspects: impulsive intensity and density. In detail, the impulsive instants and jumps are respectively impelled by a renewal process and a Markov chain. By analyzing the coupling effect among stochastic noise, randomly impulsive intensity and density, novel criteria of ES a.s. are obtained by employing Lyapunov-based approach. The proposed results not only capture the positive effect of stochastic noise, but also remove the non-zero property of solution required in existing works. As an application, the synchronization problem of master-slave stochastic chaotic systems is solved by applying the randomly impulsive control method. Two examples are provided to illustrate the effectiveness and application of the proposed results.
{"title":"Almost surely exponential stability of nonlinear stochastic systems with random impulses and its application in chaos synchronization","authors":"Zenghui Hu , Jiamin Liu , Yiming Wang , Lijie You","doi":"10.1016/j.cnsns.2026.109664","DOIUrl":"10.1016/j.cnsns.2026.109664","url":null,"abstract":"<div><div>The almost surely exponential stability (ES a.s.) is investigated for nonlinear systems subject to the effects of stochastic noises and random impulses. The randomness of impulsive effects is considered in two aspects: impulsive intensity and density. In detail, the impulsive instants and jumps are respectively impelled by a renewal process and a Markov chain. By analyzing the coupling effect among stochastic noise, randomly impulsive intensity and density, novel criteria of ES a.s. are obtained by employing Lyapunov-based approach. The proposed results not only capture the positive effect of stochastic noise, but also remove the non-zero property of solution required in existing works. As an application, the synchronization problem of master-slave stochastic chaotic systems is solved by applying the randomly impulsive control method. Two examples are provided to illustrate the effectiveness and application of the proposed results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109664"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962060","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 : 2026-01-14DOI: 10.1016/j.cnsns.2026.109643
Xiao Tang , Junwei Huang
In the present paper, we construct a new class of second-order partitioned explicit stabilized methods for the ordinary differential equations (ODEs) containing moderately stiff and non-stiff terms, which are usually obtained after the spatial semi-discretization of the time-dependent partial differential equations (PDEs). We treat the moderately stiff term with an s-stage Runge-Kutta-Chebyshev (RKC) method and treat the non-stiff term with a 4m-stage explicit Runge-Kutta (RK) method. Different from several existing partitioned explicit stabilized methods that employ fixed-stage RK methods to handle the non-stiff term, both the parameters s and m in our methods can be flexibly adjusted as needed for the problems. Numerical experiments and comparisons with several existing partitioned explicit stabilized methods show the flexibility and efficiency of our new partitioned methods.
{"title":"A class of flexible and efficient partitioned Runge-Kutta-Chebyshev methods for some time-dependent partial differential equations","authors":"Xiao Tang , Junwei Huang","doi":"10.1016/j.cnsns.2026.109643","DOIUrl":"10.1016/j.cnsns.2026.109643","url":null,"abstract":"<div><div>In the present paper, we construct a new class of second-order partitioned explicit stabilized methods for the ordinary differential equations (ODEs) containing moderately stiff and non-stiff terms, which are usually obtained after the spatial semi-discretization of the time-dependent partial differential equations (PDEs). We treat the moderately stiff term with an <em>s</em>-stage Runge-Kutta-Chebyshev (RKC) method and treat the non-stiff term with a 4<em>m</em>-stage explicit Runge-Kutta (RK) method. Different from several existing partitioned explicit stabilized methods that employ fixed-stage RK methods to handle the non-stiff term, both the parameters <em>s</em> and <em>m</em> in our methods can be flexibly adjusted as needed for the problems. Numerical experiments and comparisons with several existing partitioned explicit stabilized methods show the flexibility and efficiency of our new partitioned methods.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109643"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995143","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 : 2026-01-14DOI: 10.1016/j.cnsns.2026.109753
Yiming Shang , Guangbin Cai , Xiangwei Bu , Chaoxu Mu , Tong Wu , Hui Xu
In this paper, a novel prescribed performance sliding mode control strategy integrated with a neural network-based disturbance observer (NDO) is proposed to achieve fast and robust synchronization of chaotic systems. First, the synchronization error is transformed from the error domain (e-domain) to the performance domain (ζ-domain) by employing a prescribed performance function. Subsequently, based on the transformed error dynamics, a sliding mode surface that incorporates a delayed feedback term is designed. A synchronization controller is then developed based on the proposed sliding mode surface. To enhance system robustness against unknown disturbances, a neural network-based disturbance observer is introduced to estimate and compensate for uncertainties in real time. The stability of the closed-loop synchronization error system is rigorously proved based on the Lyapunov-Krasovskii (L-K) functional method. Finally, numerical simulation results are presented to demonstrate the effectiveness and superior performance of the proposed control strategy.
{"title":"Prescribed performance sliding mode synchronization of chaotic systems via neural network-based disturbance observer","authors":"Yiming Shang , Guangbin Cai , Xiangwei Bu , Chaoxu Mu , Tong Wu , Hui Xu","doi":"10.1016/j.cnsns.2026.109753","DOIUrl":"10.1016/j.cnsns.2026.109753","url":null,"abstract":"<div><div>In this paper, a novel prescribed performance sliding mode control strategy integrated with a neural network-based disturbance observer (NDO) is proposed to achieve fast and robust synchronization of chaotic systems. First, the synchronization error is transformed from the error domain (<em>e</em>-domain) to the performance domain (<em>ζ</em>-domain) by employing a prescribed performance function. Subsequently, based on the transformed error dynamics, a sliding mode surface that incorporates a delayed feedback term is designed. A synchronization controller is then developed based on the proposed sliding mode surface. To enhance system robustness against unknown disturbances, a neural network-based disturbance observer is introduced to estimate and compensate for uncertainties in real time. The stability of the closed-loop synchronization error system is rigorously proved based on the Lyapunov-Krasovskii (L-K) functional method. Finally, numerical simulation results are presented to demonstrate the effectiveness and superior performance of the proposed control strategy.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109753"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995148","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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