{"title":"A linearized conservative compact scheme based on the double reduction order method for the Rosenau–Burgers equation","authors":"Sitong Dong, Yiran Zhang, Yuanfeng Jin","doi":"10.1016/j.cnsns.2025.108974","DOIUrl":"10.1016/j.cnsns.2025.108974","url":null,"abstract":"<div><div>In this paper, we propose a three-level linearized difference scheme to solve the Rosenau–Burgers equation based on the double reduction order method and the fourth-order compact operator under the spatial periodic boundary conditions. We discuss the conservation law, solvability, and convergence for this difference scheme. The proposed scheme has second-order temporal and fourth-order spatial convergence. Numerical simulations are also provided which agree well with our theoretical analysis.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108974"},"PeriodicalIF":3.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222088","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}
{"title":"Non-Lie non-classical symmetry solutions of a class of nonlinear reaction–diffusion equations","authors":"David Plenty, Maureen P. Edwards","doi":"10.1016/j.cnsns.2025.108973","DOIUrl":"10.1016/j.cnsns.2025.108973","url":null,"abstract":"<div><div>Nonlinear one-dimensional reaction–diffusion equations are useful for modeling processes in science and engineering. Non-classical symmetry analysis with a vanishing coefficient of <span><math><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><mi>t</mi></mrow></mfrac></math></span> is applied to search for non-Lie solutions of a class of nonlinear reaction–diffusion equations. The analysis leads to two non-classical symmetries. Each symmetry gives a solution that cannot be constructed using classical symmetries or non-classical symmetries with a non-vanishing coefficient of <span><math><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><mi>t</mi></mrow></mfrac></math></span>. A solution is presented as a potential model for population growth in biology.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108973"},"PeriodicalIF":3.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264001","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}
Yangang Yao , Yu Kang , Yunbo Zhao , Jieqing Tan , Lichuan Gu , Chao Wang
{"title":"Event-based uniform prescribed-time output feedback control for irregular output-constrained nonlinear systems","authors":"Yangang Yao , Yu Kang , Yunbo Zhao , Jieqing Tan , Lichuan Gu , Chao Wang","doi":"10.1016/j.cnsns.2025.109010","DOIUrl":"10.1016/j.cnsns.2025.109010","url":null,"abstract":"<div><div>This paper proposes an event-based uniform prescribed-time output feedback control (PTOFC) approach for irregular output-constrained nonlinear systems (OCNSs). Unlike the most existing methods of OCNSs, they mainly focus on OCNSs with infinite-time/deferred output constraints (i.e., the output constraints existing for all <span><math><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math></span> or <span><math><mrow><mi>t</mi><mo>≥</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>), while many actual systems often suffer from irregular output constraints (including infinite-time constraints, deferred constraints, unconstrained, constrained and unconstrained alternations, etc.), leading to new challenges in control design. By devising a stretch model-based nonlinear mapping function, and combining with event trigger control (ETC) technique, an event-based unified output feedback control algorithm is proposed, and the significant advantage is its suitability for infinite-time/deferred/alternant OCNSs, as well as unconstrained systems, without necessitating modifications to the control structure, and the communication burden is also effectively reduced. Furthermore, with the aid of the scaling transformation function (STF)-based prescribed-time stability (PTS) criteria, a novel prescribed-time state observer (PTSO)-based PTOFC algorithm is designed, under which the settling time can be pre-set arbitrarily regardless of the initial system states and control parameters. Meanwhile, the problems of singularity and large initial control input in conventional prescribed-time control schemes are eliminated. The presented approach is verified by means of simulation examples.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 109010"},"PeriodicalIF":3.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222093","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}
{"title":"Bifurcation dynamics of a predator–prey model with impulsive density-dependent nonlinear pesticide spraying and predator release","authors":"Zeli Zhou , Qi Quan , Jianjun Jiao , Xiangjun Dai","doi":"10.1016/j.cnsns.2025.108979","DOIUrl":"10.1016/j.cnsns.2025.108979","url":null,"abstract":"<div><div>In this study, we propose a predator–prey model incorporating impulsive density-dependent nonlinear pesticide spraying and the release of predators (natural enemy of the pest) at different fixed moments. The pest extinction semi-trivial periodic solution is derived. Further, global asymptotic stability of the obtained periodic solution and the permanence of the studied model are acquired. Depending on the maximum number of pest natural enemies released impulsively, the threshold for pest extinction is derived. By considering the impulsive period as a bifurcation parameter, the condition for a supercritical bifurcation in the system is obtained. To verify the correctness of the results obtained in this paper, study the impact of key parameters on the pest extinction threshold condition, and explore more complex dynamic behaviors of the model, numerical simulations are conducted. These simulations demonstrate that the optimal impulsive control period varies for different pest management strategies. Moreover, the maximum release quantity of natural enemies, the impulsive control period, and the maximal fatality rate of pesticide for pest significantly influence the dynamic behaviors of the model. The results presented in this paper offer significant theoretical implications for integrated pest management.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108979"},"PeriodicalIF":3.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222091","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}
{"title":"KAM theorems for nonlinear higher dimensional Schrödinger equation systems in three different ways","authors":"Ningning Chang , Yingnan Sun","doi":"10.1016/j.cnsns.2025.108981","DOIUrl":"10.1016/j.cnsns.2025.108981","url":null,"abstract":"<div><div>We prove an abstract KAM (Kolmogorov–Arnold–Moser) theorem constructed by Zhou (2017) in different ways and apply it to the nonlinear Schrödinger equation systems with real Fourier Multiplier. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions for more types of equation systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108981"},"PeriodicalIF":3.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241646","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}
{"title":"Node center identification in complex networks based on Jensen–Shannon divergence","authors":"Bowen Han, Guochen Feng, Pengjian Shang","doi":"10.1016/j.cnsns.2025.108977","DOIUrl":"10.1016/j.cnsns.2025.108977","url":null,"abstract":"<div><div>The evaluation of node centrality remains a critical challenge in the field of complex network research. This paper proposes a novel method, the <span><math><mrow><mi>J</mi><mi>S</mi><mi>D</mi></mrow></math></span> method, which integrates local and global information to measure node centrality. The method employs Shannon entropy to quantify local centrality and Jensen–Shannon (<span><math><mrow><mi>J</mi><mi>S</mi></mrow></math></span>) divergence to compute inter-community distances, thereby assessing topological differences between communities and measuring global centrality. Experiments conducted on both real and random networks evaluated the impact of central nodes identified by the <span><math><mrow><mi>J</mi><mi>S</mi><mi>D</mi></mrow></math></span> method on network efficiency. Simulation results demonstrate that in networks with distinct community structures, the <span><math><mrow><mi>J</mi><mi>S</mi><mi>D</mi></mrow></math></span> method provides more accurate node centrality measurements compared to the <span><math><mrow><mi>B</mi><mi>C</mi></mrow></math></span>, <span><math><mrow><mi>C</mi><mi>C</mi><mi>I</mi></mrow></math></span>, <span><math><mrow><mi>C</mi><mi>B</mi><mi>C</mi></mrow></math></span>, <span><math><mrow><mi>C</mi><mi>O</mi><mi>M</mi><mi>M</mi></mrow></math></span>, and <span><math><mrow><mi>C</mi><mi>I</mi></mrow></math></span> methods. Additionally, the repetition frequency of central ranking nodes indicates that the <span><math><mrow><mi>J</mi><mi>S</mi><mi>D</mi></mrow></math></span> method effectively distinguishes the centrality of different nodes. Finally, the paper discusses the impact of different combination methods on measurement performance, revealing that incorporating additional community information further enhances the method’s effectiveness.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108977"},"PeriodicalIF":3.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144252911","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}
{"title":"Distributed fault detection for a class of network systems: Optimal unknown input observer design","authors":"Ya-Jun Tang , Xiao-Jian Li","doi":"10.1016/j.cnsns.2025.108976","DOIUrl":"10.1016/j.cnsns.2025.108976","url":null,"abstract":"<div><div>This paper is concerned with the fault detection problem for a class of network systems composed of multiple clusters with unknown system matrices. Each cluster consists of multiple subsystems and the connections between clusters are unmeasurable. For these unmeasurable connections in network systems, traditional system identification and fault detection methods may be difficult to be directly applied. To solve this problem, the subspace instrumental variable method is proposed under the distributed framework, which utilizes the intersection of subspaces on local observations as the states of connections to further identify the local cluster subsystem matrices. Based on the result of identification, the unknown input observer (UIO) is then designed to detect the faults of local cluster systems. However, these connections also lead to the rank conditions for designing UIO not being satisfied. Thus, the unknown input decomposition approach is presented to address this problem, such that the decouplable part is eliminated from the error system and the impact of undecouplable part is attenuated by robust performance index. Finally, the effectiveness and advantages of the proposed fault detection scheme are verified via numerical simulation and comparative analysis.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108976"},"PeriodicalIF":3.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222092","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}
{"title":"Hyperbolic structure for multiplicative noise saddle using Lagrangian descriptors","authors":"Huan Liao , Jiaopeng Yang","doi":"10.1016/j.cnsns.2025.108971","DOIUrl":"10.1016/j.cnsns.2025.108971","url":null,"abstract":"<div><div>This paper proposes a new concept, continuous stochastic Lagrangian descriptor, to discern the hyperbolic structure for multiplicative noise saddle and beyond. The multiplicative noise saddle is proved to entail a random fixed point with exponential dichotomy. Analogous to the additive noise case, the hyperbolic structures, composed of the random fixed point together with its stable and unstable manifolds, form barriers to transport in such a system. Moreover, the forward and backward components are compared to show the visible stable and/or unstable manifolds. We further discuss the capability of the discrete stochastic Lagrangian descriptor with the stochastic forced Duffing equation for the general systems driven by multiplicative noise.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108971"},"PeriodicalIF":3.4,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222089","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}
{"title":"Hamilton–Pfaff type PDEs through multi-dimensional fractional optimization problems","authors":"Octavian Postavaru , Antonela Toma , Savin Treanţă","doi":"10.1016/j.cnsns.2025.108969","DOIUrl":"10.1016/j.cnsns.2025.108969","url":null,"abstract":"<div><div>In this paper, we derive Hamilton–Pfaff-type partial differential equations (PDEs) by employing exterior differential techniques within the framework of a multi-dimensional fractional optimal control problem, incorporating principles from fractional calculus. This approach provides a rigorous analytical foundation for studying systems governed by non-integer order dynamics, thereby enhancing the understanding of complex control processes. By formulating a control Hamiltonian 1-form associated with the underlying fractional optimal control problem and its corresponding adjoint distributions, we systematically derive the Hamilton–Pfaff-type PDEs. These equations capture the intricate relationship between fractional dynamics and optimal control, paving the way for further investigation of sophisticated systems in a wide range of applications.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108969"},"PeriodicalIF":3.4,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205083","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}
{"title":"Hidden memory chaotic attractors in simple nonequilibrium fractional order systems","authors":"Bichitra Kumar Lenka, Ranjit Kumar Upadhyay","doi":"10.1016/j.cnsns.2025.108970","DOIUrl":"10.1016/j.cnsns.2025.108970","url":null,"abstract":"<div><div>A computational bifurcation diagram of nonlinear fractional order systems may provide a visual representation of understanding possible dynamics in a wide range of system parameters and associated fractional orders. This observed phenomenon has sparked new interest in the question of mathematically sound and rigorous proofs of the existence of such dynamics. No mathematical foundation for the stability of bifurcations has been developed for fractional order systems, and roughly computational attractors are less understood. A famous hidden memory chaotic attractor is the typical class of attractor that does occur in nonlinear fractional order systems without any known bifurcations of any existing attractors. It has been found that such attractors are fundamental and localized with nonlinear fractional-order systems with no equilibrium points. Many intuitive examples are constructed, and the governing dynamics are hidden memory chaotic attractors.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108970"},"PeriodicalIF":3.4,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205084","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}