Pub Date : 2024-11-01DOI: 10.1016/j.cnsns.2024.108422
Xin Liu , Lili Chen , Yanfeng Zhao , Zhen Wang
In this paper, the exponential synchronization problem for fractional-order T–S fuzzy complex multi-links networks under an intermittent dynamic event-triggered control (IDE-TC) strategy is discussed. To this end, a new triggering rule with a dynamical variable is first introduced, including some available static triggering rules as its particular form. Then, it is proved that the applied dynamical variable is positive by using some properties of the Mittag-Leffler function. Hence, the inter-event time between any two successive triggering moments can be enlarged than static event-triggered results. Additionally, there is a guaranteed positive minimum inter-event time for each sample path solution of systems. Based on the Lyapunov method and the graph theory, exponential synchronization criteria of the proposed networks under the IDE-TC strategy is deduced. Finally, the validity and feasibility of the derived theoretical results are investigated by an application with simulations.
{"title":"Exponential synchronization of fractional-order T–S fuzzy complex multi-links networks with intermittent dynamic event-triggered control","authors":"Xin Liu , Lili Chen , Yanfeng Zhao , Zhen Wang","doi":"10.1016/j.cnsns.2024.108422","DOIUrl":"10.1016/j.cnsns.2024.108422","url":null,"abstract":"<div><div>In this paper, the exponential synchronization problem for fractional-order T–S fuzzy complex multi-links networks under an intermittent dynamic event-triggered control (IDE-TC) strategy is discussed. To this end, a new triggering rule with a dynamical variable is first introduced, including some available static triggering rules as its particular form. Then, it is proved that the applied dynamical variable is positive by using some properties of the Mittag-Leffler function. Hence, the inter-event time between any two successive triggering moments can be enlarged than static event-triggered results. Additionally, there is a guaranteed positive minimum inter-event time for each sample path solution of systems. Based on the Lyapunov method and the graph theory, exponential synchronization criteria of the proposed networks under the IDE-TC strategy is deduced. Finally, the validity and feasibility of the derived theoretical results are investigated by an application with simulations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587089","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 : 2024-10-29DOI: 10.1016/j.cnsns.2024.108407
Sitao Zhang , Lin Liu , Zhixia Ge , Yu Liu , Libo Feng , Jihong Wang
This paper mainly contributes to investigating a distinctive fractional Schrödinger equation (FSE) for describing the quantum dynamics on a comb. The special characteristic of the comb is that the diffusion versus the -direction only occurs on the -axis. We replace the infinite boundary with the absorbing boundary conditions (ABCs), which can be obtained using the Laplace transform. We utilize the integration property to deal with the singularity function in the FSE and propose the finite difference method. The stability and convergence of this scheme are investigated. The scheme to discretize the Caputo fractional derivative needs a particularly expensive computational and storage cost. To increase the calculation speed, a fast algorithm is used to improve the operation efficiency. By introducing a source term, the exact solution and the numerical solution are compared. The comparison of the CPU time for the scheme and fast scheme is given. The comparison between the FSE on a comb and the classical one is also analyzed and discussed. The transport process versus the -axis and the -axis with various parameters are shown. Finally, the mean square displacement (MSD) is investigated. We find that the solution with the ABCs has a better agreement with the exact expression compared to the solution with truncated zero boundary conditions.
本文主要致力于研究一种独特的分数薛定谔方程（FSE），用于描述梳子上的量子动力学。梳状体的特殊性在于，相对于 x 方向的扩散只发生在 x 轴上。我们用吸收边界条件（ABCs）取代了无限边界，它可以通过拉普拉斯变换得到。我们利用积分特性来处理 FSE 中的奇异函数，并提出了有限差分法。我们对该方法的稳定性和收敛性进行了研究。对 Caputo 分数导数进行离散化的 L1 方案需要特别昂贵的计算和存储成本。为了提高计算速度，采用了一种快速算法来提高运算效率。通过引入源项，比较了精确解和数值解。比较了 L1 方案和快速方案的 CPU 时间。此外，还分析和讨论了梳子上的 FSE 与经典 FSE 的比较。图中显示了不同参数下的传输过程与 x 轴和 y 轴的关系。最后，研究了均方位移（MSD）。我们发现，与采用截断零边界条件的解法相比，采用 ABC 的解法与精确表达式的一致性更好。
{"title":"Numerical simulation of the two-dimensional fractional Schrödinger equation for describing the quantum dynamics on a comb with the absorbing boundary conditions","authors":"Sitao Zhang , Lin Liu , Zhixia Ge , Yu Liu , Libo Feng , Jihong Wang","doi":"10.1016/j.cnsns.2024.108407","DOIUrl":"10.1016/j.cnsns.2024.108407","url":null,"abstract":"<div><div>This paper mainly contributes to investigating a distinctive fractional Schrödinger equation (FSE) for describing the quantum dynamics on a comb. The special characteristic of the comb is that the diffusion versus the <span><math><mi>x</mi></math></span>-direction only occurs on the <span><math><mi>x</mi></math></span>-axis. We replace the infinite boundary with the absorbing boundary conditions (ABCs), which can be obtained using the Laplace transform. We utilize the integration property to deal with the singularity function in the FSE and propose the finite difference method. The stability and convergence of this scheme are investigated. The <span><math><mi>L1</mi></math></span> scheme to discretize the Caputo fractional derivative needs a particularly expensive computational and storage cost. To increase the calculation speed, a fast algorithm is used to improve the operation efficiency. By introducing a source term, the exact solution and the numerical solution are compared. The comparison of the CPU time for the <span><math><mi>L1</mi></math></span> scheme and fast scheme is given. The comparison between the FSE on a comb and the classical one is also analyzed and discussed. The transport process versus the <span><math><mi>x</mi></math></span>-axis and the <span><math><mi>y</mi></math></span>-axis with various parameters are shown. Finally, the mean square displacement (MSD) is investigated. We find that the solution with the ABCs has a better agreement with the exact expression compared to the solution with truncated zero boundary conditions.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587088","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 : 2024-10-29DOI: 10.1016/j.cnsns.2024.108425
Shuai Mo , Xuan Huang , Wenbin Liu , Yuansheng Zhou , Jielu Zhang , Haruo Houjoh , Wei Zhang
Mechanical metamaterials with tunable mechanical properties have received extensive attention. In this work, a continuous steady-state metamaterial with tunable mechanical based on planetary gear cells is designed. Firstly, the excellent tunable properties of metamaterials are studied, which shows the designed metamaterials has a wide range of programmable stiffness and a significantly tunning band gap. The configuration relationship between tunability and structural parameters is analyzed. Then, a rigid-flexible coupling nonlinear dynamic model of planetary gear metamaterials is established and the dynamic characteristics of planetary gear metamaterials in the process of dynamic tunning are explored by numerical simulation. Moreover, the distribution characteristics of the system vibration response with the coupling parameter plane are disclosed, and the influence of the system dynamic parameters on its bifurcation characteristics and stability under coupling excitation is explored. Furthermore, an improved non-iterative cell mapping method is used to analyze the dependence of the vibration response of the system on the initial conditions. This work shows that the planetary gear metamaterials have a wide range of stiffness tunability and significantly variable band gap interval. Under the influences of internal and external excitations, the system exhibits various dynamic characteristics. The dynamic characteristics of flexible construction are mainly affected by structural parameters, and the dynamic characteristics of rigid construction are affected by multiple sets of coupling parameters and initial conditions.
{"title":"Nonlinear dynamics of continuous steady-state tunable mechanical metamaterials based on planetary gears","authors":"Shuai Mo , Xuan Huang , Wenbin Liu , Yuansheng Zhou , Jielu Zhang , Haruo Houjoh , Wei Zhang","doi":"10.1016/j.cnsns.2024.108425","DOIUrl":"10.1016/j.cnsns.2024.108425","url":null,"abstract":"<div><div>Mechanical metamaterials with tunable mechanical properties have received extensive attention. In this work, a continuous steady-state metamaterial with tunable mechanical based on planetary gear cells is designed. Firstly, the excellent tunable properties of metamaterials are studied, which shows the designed metamaterials has a wide range of programmable stiffness and a significantly tunning band gap. The configuration relationship between tunability and structural parameters is analyzed. Then, a rigid-flexible coupling nonlinear dynamic model of planetary gear metamaterials is established and the dynamic characteristics of planetary gear metamaterials in the process of dynamic tunning are explored by numerical simulation. Moreover, the distribution characteristics of the system vibration response with the coupling parameter plane are disclosed, and the influence of the system dynamic parameters on its bifurcation characteristics and stability under coupling excitation is explored. Furthermore, an improved non-iterative cell mapping method is used to analyze the dependence of the vibration response of the system on the initial conditions. This work shows that the planetary gear metamaterials have a wide range of stiffness tunability and significantly variable band gap interval. Under the influences of internal and external excitations, the system exhibits various dynamic characteristics. The dynamic characteristics of flexible construction are mainly affected by structural parameters, and the dynamic characteristics of rigid construction are affected by multiple sets of coupling parameters and initial conditions.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578209","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 : 2024-10-29DOI: 10.1016/j.cnsns.2024.108426
Minge Yang , Junyi He , Qiqing Yue , Hua Tang
This paper presents a comprehensive study of the nonlinear dynamic behavior and snap-through phenomena in sandwich arch structures with viscoelastic cores and carbon nanotube-reinforced nanocomposite face sheets. Subjected to uniform time-dependent pressure shocks, these arches exhibit complex snap-through behavior critical for practical engineering applications. Utilizing third-order shear deformation theory, the study accurately captures nonlinear behaviors. The viscoelastic core, modeled with the Kelvin-Voigt law, enhances damping and reduces vibration amplitudes. Numerical solutions are obtained using a Chebyshev-based Ritz method, Newmark integration, and Newton-Raphson method. The Budiansky-Ruth criterion evaluates dynamic buckling loads. Key findings include significant instability near buckling loads, increased buckling loads and vibration damping due to viscoelastic effects, reduced buckling loads with foam cores, improved performance with CNTs, and more pronounced CNT effects with greater deflections. Additional conclusions highlight the sensitivity of dynamic snap-through to geometric parameters and the superior accuracy of the proposed approach compared to traditional models. This research advances the understanding and design strategies for nonlinear sandwich arch structures, enhancing predictive capabilities in complex structural systems.
{"title":"Dynamic instability and nonlinear response analysis of nanocomposite sandwich arches with viscoelastic cores","authors":"Minge Yang , Junyi He , Qiqing Yue , Hua Tang","doi":"10.1016/j.cnsns.2024.108426","DOIUrl":"10.1016/j.cnsns.2024.108426","url":null,"abstract":"<div><div>This paper presents a comprehensive study of the nonlinear dynamic behavior and snap-through phenomena in sandwich arch structures with viscoelastic cores and carbon nanotube-reinforced nanocomposite face sheets. Subjected to uniform time-dependent pressure shocks, these arches exhibit complex snap-through behavior critical for practical engineering applications. Utilizing third-order shear deformation theory, the study accurately captures nonlinear behaviors. The viscoelastic core, modeled with the Kelvin-Voigt law, enhances damping and reduces vibration amplitudes. Numerical solutions are obtained using a Chebyshev-based Ritz method, Newmark integration, and Newton-Raphson method. The Budiansky-Ruth criterion evaluates dynamic buckling loads. Key findings include significant instability near buckling loads, increased buckling loads and vibration damping due to viscoelastic effects, reduced buckling loads with foam cores, improved performance with CNTs, and more pronounced CNT effects with greater deflections. Additional conclusions highlight the sensitivity of dynamic snap-through to geometric parameters and the superior accuracy of the proposed approach compared to traditional models. This research advances the understanding and design strategies for nonlinear sandwich arch structures, enhancing predictive capabilities in complex structural systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578208","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 : 2024-10-29DOI: 10.1016/j.cnsns.2024.108404
Hui Cao , Jianquan Li , Pei Yu
A simple mathematical model describing the immune response during the stage latent tuberculosis infection is established and analyzed. The main purpose of this study is to explore the sustained immune response of the immune system against invaded Mycobacterium tuberculosis in the stage of latent tuberculosis infection. First, the threshold is defined to determine the occurrence of sustained immune response. Then, stability conditions are derived to show that the sustained immune response may converge to a constant or to a stable periodical oscillation, implying that the Mycobacterium tuberculosis, the infected macrophages, the activated uninfected macrophages, and the immune cells coexist to form the tuberculous granuloma structure. This structure may appear calcified if the system solution converges to a constant, or maintains a dynamic balance if the system solution undergoes a periodical oscillation. These findings well demonstrate the process of sustained immune response in the latent tuberculosis infection as the Mycobacterium tuberculosis is changing. Numerical examples are presented to illustrate the theoretical predictions.
{"title":"Study of immune response in a latent tuberculosis infection model","authors":"Hui Cao , Jianquan Li , Pei Yu","doi":"10.1016/j.cnsns.2024.108404","DOIUrl":"10.1016/j.cnsns.2024.108404","url":null,"abstract":"<div><div>A simple mathematical model describing the immune response during the stage latent tuberculosis infection is established and analyzed. The main purpose of this study is to explore the sustained immune response of the immune system against invaded Mycobacterium tuberculosis in the stage of latent tuberculosis infection. First, the threshold <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is defined to determine the occurrence of sustained immune response. Then, stability conditions are derived to show that the sustained immune response may converge to a constant or to a stable periodical oscillation, implying that the Mycobacterium tuberculosis, the infected macrophages, the activated uninfected macrophages, and the immune cells coexist to form the tuberculous granuloma structure. This structure may appear calcified if the system solution converges to a constant, or maintains a dynamic balance if the system solution undergoes a periodical oscillation. These findings well demonstrate the process of sustained immune response in the latent tuberculosis infection as the Mycobacterium tuberculosis is changing. Numerical examples are presented to illustrate the theoretical predictions.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572687","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 : 2024-10-28DOI: 10.1016/j.cnsns.2024.108401
Julia Calatayud , Marc Jornet , Carla M.A. Pinto
A random differential equation, or stochastic differential equation with parametric uncertainty, is a classical differential equation whose input values (coefficients, initial conditions, etc.) are random variables. Given data, the probability distributions of the input random parameters must be appropriately inferred, before proceeding to simulate the model’s output. This task is called inverse uncertainty quantification. In this paper, the goal is to study the applicability of the Bayesian bootstrap to draw inferences on the posterior distributions of the parameters, by resampling the residuals of the deterministic least-squares optimization with Dirichlet weights. The method is based on repeated deterministic calibrations. Thus, to alleviate the curse of dimensionality, the technique may be combined with the principle of maximum entropy for densities, when there are some parameters that are not optimized deterministically. For illustration of the methodology, two case studies on important health topics are conducted, with stochastic fitting to data. The first one, on past alcohol consumption in Spain, taking social contagion into account. The second one, on HIV evolution considering CD4 T cells and viral load, with a patient in clinical follow-up. All these applied models are built from a compartmental viewpoint, with a randomized basic reproduction number that controls the long-term behavior of the system.
随机微分方程或具有参数不确定性的随机微分方程，是一种输入值（系数、初始条件等）为随机变量的经典微分方程。给定数据后，必须适当推断输入随机参数的概率分布，然后再模拟模型的输出。这项任务称为反向不确定性量化。本文的目标是研究贝叶斯自举法的适用性，通过对确定性最小二乘优化的残差进行重采样，利用 Dirichlet 权重推断参数的后验分布。该方法以重复确定性校准为基础。因此，为了减轻维度诅咒，当有一些参数无法进行确定性优化时，该技术可与密度的最大熵原理相结合。为了说明该方法，我们对重要的健康主题进行了两个案例研究，并对数据进行了随机拟合。第一个案例是关于西班牙过去的酒精消费情况，考虑了社会传染因素。第二个案例是关于艾滋病毒的演变，考虑了 CD4+ T 细胞和病毒载量，并对一名患者进行了临床随访。所有这些应用模型都是从分区的角度建立的，其随机基本繁殖数控制着系统的长期行为。
{"title":"Inverse uncertainty quantification for stochastic systems by resampling. Applications to modeling of alcohol consumption and infection by HIV","authors":"Julia Calatayud , Marc Jornet , Carla M.A. Pinto","doi":"10.1016/j.cnsns.2024.108401","DOIUrl":"10.1016/j.cnsns.2024.108401","url":null,"abstract":"<div><div>A random differential equation, or stochastic differential equation with parametric uncertainty, is a classical differential equation whose input values (coefficients, initial conditions, etc.) are random variables. Given data, the probability distributions of the input random parameters must be appropriately inferred, before proceeding to simulate the model’s output. This task is called inverse uncertainty quantification. In this paper, the goal is to study the applicability of the Bayesian bootstrap to draw inferences on the posterior distributions of the parameters, by resampling the residuals of the deterministic least-squares optimization with Dirichlet weights. The method is based on repeated deterministic calibrations. Thus, to alleviate the curse of dimensionality, the technique may be combined with the principle of maximum entropy for densities, when there are some parameters that are not optimized deterministically. For illustration of the methodology, two case studies on important health topics are conducted, with stochastic fitting to data. The first one, on past alcohol consumption in Spain, taking social contagion into account. The second one, on HIV evolution considering CD4<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells and viral load, with a patient in clinical follow-up. All these applied models are built from a compartmental viewpoint, with a randomized basic reproduction number that controls the long-term behavior of the system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554126","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 : 2024-10-24DOI: 10.1016/j.cnsns.2024.108403
Zbigniew Galias
Modification of a parameter of a chaotic system may lead to the emergence of a periodic attractor. Under certain assumptions periodic windows (regions in the parameter space in which a periodic attractor exists) densely fill a chaotic region. Usually it is very difficult to prove this property. In this work, we propose a systematic procedure to locate and prove the existence of periodic windows. The method combines the symbolic dynamics based approach to find unstable periodic orbits (UPOs), the continuation method to locate periodic windows (PWs), and interval arithmetic tools to prove their existence. The proposed method is applied to the Rössler system. The existence of several thousands of PWs close to the classical parameter values is proved and periodic attractors very close in the parameter space to the classical Rössler attractor are found. Estimates of measures of sets of parameters for which a periodic attractor exists are calculated.
{"title":"Symbolic dynamics approach to find periodic windows: The case study of the Rössler system","authors":"Zbigniew Galias","doi":"10.1016/j.cnsns.2024.108403","DOIUrl":"10.1016/j.cnsns.2024.108403","url":null,"abstract":"<div><div>Modification of a parameter of a chaotic system may lead to the emergence of a periodic attractor. Under certain assumptions periodic windows (regions in the parameter space in which a periodic attractor exists) densely fill a chaotic region. Usually it is very difficult to prove this property. In this work, we propose a systematic procedure to locate and prove the existence of periodic windows. The method combines the symbolic dynamics based approach to find unstable periodic orbits (UPOs), the continuation method to locate periodic windows (PWs), and interval arithmetic tools to prove their existence. The proposed method is applied to the Rössler system. The existence of several thousands of PWs close to the classical parameter values is proved and periodic attractors very close in the parameter space to the classical Rössler attractor are found. Estimates of measures of sets of parameters for which a periodic attractor exists are calculated.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572688","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 : 2024-10-24DOI: 10.1016/j.cnsns.2024.108400
Renjie Han , Yezi Xu , Hao Fu , Dong Yan
In this work, by utilizing the Strang splitting technique, some advanced conformal structure-preserving schemes are developed for solving the damped nonlinear Schrödinger equation (DNLSE). The proposed innovative numerical approaches, namely the high-order compact conformal multi-symplectic method and the conformal momentum-preserving method, have two key computational advantages. Firstly, these two approaches excel in conserving local structures, and more importantly, they are capable of maintaining exact energy dissipation rates in any time-space region, particularly under periodic boundary conditions. To validate the theoretical properties and demonstrate the efficacy and stability of these approaches in long-time integrations, we conduct through extensive numerical simulations involving both bright and dark solitons.
{"title":"Novel conformal structure-preserving schemes for the linearly damped nonlinear Schrödinger equation","authors":"Renjie Han , Yezi Xu , Hao Fu , Dong Yan","doi":"10.1016/j.cnsns.2024.108400","DOIUrl":"10.1016/j.cnsns.2024.108400","url":null,"abstract":"<div><div>In this work, by utilizing the Strang splitting technique, some advanced conformal structure-preserving schemes are developed for solving the damped nonlinear Schrödinger equation (DNLSE). The proposed innovative numerical approaches, namely the high-order compact conformal multi-symplectic method and the conformal momentum-preserving method, have two key computational advantages. Firstly, these two approaches excel in conserving local structures, and more importantly, they are capable of maintaining exact energy dissipation rates in any time-space region, particularly under periodic boundary conditions. To validate the theoretical properties and demonstrate the efficacy and stability of these approaches in long-time integrations, we conduct through extensive numerical simulations involving both bright and dark solitons.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554127","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 : 2024-10-23DOI: 10.1016/j.cnsns.2024.108399
S.S. Mohanrasu , T.M.C. Priyanka , A. Gowrisankar , Ardak Kashkynbayev , K. Udhayakumar , R. Rakkiyappan
The purpose of this research is twofold. First, the master–slave synchronization of fractional-order neural networks is explored with time delays using aperiodic intermittent control. Then we present a sufficient condition for master–slave synchronization of delayed fractional-order neural networks via average-width intermittent control technique. A numerical simulation is used to demonstrate the efficacy of the derived results. Second, a novel investigation of the Caputo-fractional derivative of Hermite fractal splines is accomplished. Moreover, its box counting dimension is estimated and related with the Caputo-fractional order. Additionally, we propose an image encryption algorithm utilizing the semi-tensor product (STP). The efficiency of the algorithm is evaluated through the application of statistical measures.
{"title":"Fractional derivative of Hermite fractal splines on the fractional-order delayed neural networks synchronization","authors":"S.S. Mohanrasu , T.M.C. Priyanka , A. Gowrisankar , Ardak Kashkynbayev , K. Udhayakumar , R. Rakkiyappan","doi":"10.1016/j.cnsns.2024.108399","DOIUrl":"10.1016/j.cnsns.2024.108399","url":null,"abstract":"<div><div>The purpose of this research is twofold. First, the master–slave synchronization of fractional-order neural networks is explored with time delays using aperiodic intermittent control. Then we present a sufficient condition for master–slave synchronization of delayed fractional-order neural networks via average-width intermittent control technique. A numerical simulation is used to demonstrate the efficacy of the derived results. Second, a novel investigation of the Caputo-fractional derivative of Hermite fractal splines is accomplished. Moreover, its box counting dimension is estimated and related with the Caputo-fractional order. Additionally, we propose an image encryption algorithm utilizing the semi-tensor product (STP). The efficiency of the algorithm is evaluated through the application of statistical measures.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535994","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 : 2024-10-22DOI: 10.1016/j.cnsns.2024.108405
Morteza Akbari , Abbas-Ali Zamani , Mohammad Seifi , Bartolomeo Pantò , Tomasz Falborski , Robert Jankowski
This paper presents an optimal nonlinear fractional-order controller (ONFOC) designed to reduce the seismic responses of tall buildings equipped with a base-isolation (BI) system and friction-tuned mass dampers (FTMDs). The parameters for the BI and FTMD systems, as well as their combinations (BI-FTMD and active BI-FTMD or ABI-FTMD), were optimized separately using a multi-objective quantum-inspired seagull optimization algorithm (MOQSOA). The seismic performances of the BI, FTMD, BI-FTMD, and ABI-FTMD systems for a 15-storey building subjected to two far-field (Loma Prieta and Landers) and two near-fields (Tabas and Northridge) earthquakes were evaluated. The results indicated that structures with BI, FTMD, BI-FTMD, and ABI-FTMD systems outperformed the uncontrolled structure in reducing structural responses during the design earthquakes (Loma Prieta and Tabas). However, under validation earthquakes (Landers and Northridge), the peak acceleration of the building with the FTMD system was worse than that of the uncontrolled structure during the near-field Northridge earthquake. To address this issue, we proposed a combination of the active BI system and the FTMD system. Time history analysis results demonstrated that for the building equipped with the ABI-FTMD system, the peak displacement, peak acceleration, and peak inter-storey drift were reduced by approximately 60%, 64%, and 78%, respectively, as compared to the uncontrolled structure.
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