Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Stability analysis of random fractional-order nonlinear systems and its application","authors":"","doi":"10.1016/j.cnsns.2024.108342","DOIUrl":"10.1016/j.cnsns.2024.108342","url":null,"abstract":"<div><p>The research on stability analysis and control design for random nonlinear systems have been greatly popularized in recent ten years, but almost no literature focuses on the fractional-order case. This paper explores the stability problem for a class of random Caputo fractional-order nonlinear systems. As a prerequisite, under the globally and the locally Lipschitz conditions, it is shown that such systems have a global unique solution with the aid of the generalized Gronwall inequality and a Picard iterative technique. By resorting to Laplace transformation and Lyapunov stability theory, some feasible conditions are established such that the considered fractional-order nonlinear systems are respectively Mittag-Leffler noise-to-state stable, Mittag-Leffler globally asymptotically stable. Then, a tracking control strategy is established for a class of random Caputo fractional-order strict-feedback systems. The feasibility analysis is addressed according to the established stability criteria. Finally, a power system and a mass–spring-damper system modeled by the random fractional-order method are employed to demonstrate the efficiency of the established analysis approach. More critically, the deficiency in the existing literatures is covered up by the current work and a set of new theories and methods in studying random Caputo fractional-order nonlinear systems is built up.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005276/pdfft?md5=ed9aabaf2f84cbf6556be1c427f5ec5f&pid=1-s2.0-S1007570424005276-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coyote and Badger Optimization (CBO): A natural inspired meta-heuristic algorithm based on cooperative hunting","authors":"","doi":"10.1016/j.cnsns.2024.108333","DOIUrl":"10.1016/j.cnsns.2024.108333","url":null,"abstract":"<div><p>Optimization techniques play a pivotal role in refining problem-solving methods across various domains. These methods have demonstrated their efficacy in addressing real-world complexities. Continuous efforts are made to create and enhance techniques in the realm of research. This paper introduces a novel technique that distinguishes itself through its clarity, logical mathematical structure, and robust mathematical equations, particularly in the second phase. This study presents the development of a new metaheuristic algorithm named Coyote and Badger Optimization (CBO). CBO draws inspiration from the cooperative behaviors observed in honey badgers and coyotes, with a specific focus on their intriguing communication process. Utilizing the inherent traits of these animals, the proposed CBO algorithm offers an intuitive and effective solution for addressing engineering optimization challenges by providing the best fitness values. To validate CBO's effectiveness in real-time applications, complex engineering problems called pressure vessel design, feature selection in medical system, and tension-compression spring design are used as case studies for testing the proposed CBO compared to other recent algorithms. Additionally, ten benchmark functions and also statistical analysis methods (mean, standard deviation, confidence intervals, <em>t</em>-test, and Wilcoxon test) are used. Experimental results demonstrate that the CBO algorithm surpasses eleven recent algorithms when subjected to common ten benchmark functions. Additionally, CBO outperforms other recent eleven algorithms according to three different case studies. According to the ten benchmark functions (F1 to F10), CBO provides the minimum fitness values which are closed to the exact (standard) values; 0, 0, 0.003, 0.0002, -1.0316, 3.0058, 0.398, 0.02, 0.00076, and 0.000725 respectively. Related to statistical analysis, CBO provides the best mean, standard deviation, confidence intervals, <em>t</em>-test, and Wilcoxon test values. According to case studies, CBO provided the minimum cost value for pressure vessel design, the maximum accuracy value for feature selection, and the minimum cost value for spring design. Hence, CBO superiors other recent algorithms.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005185/pdfft?md5=37224140d04a09ccfa0f8dd066415df0&pid=1-s2.0-S1007570424005185-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical properties of a stochastic tumor–immune model with comprehensive pulsed therapy","authors":"","doi":"10.1016/j.cnsns.2024.108330","DOIUrl":"10.1016/j.cnsns.2024.108330","url":null,"abstract":"<div><p>In this paper, a stochastic tumor–immune model with comprehensive pulsed therapy is established by taking stochastic perturbation and pulsed effect into account. Some properties of the model solutions are given in the form of the Theorems. Firstly, we obtain the equivalent solutions of the tumor–immune system by through three auxiliary equations, and prove the system solutions are existent, positive and unique. Secondly, a Lyapunov function is constructed to prove the global attraction in the mean sense for the system solution, and the boundness of the solutions’ expectation is proved by the comparison theorem of the impulsive differential equations. Next, the sufficient conditions for the extinction and non-mean persistence of tumor cells, hunting T-cells and helper T-cells, as well as the weak persistence and stochastic persistence of the tumor, are obtained by way of combining It<span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>’s differential rule and strong law of large numbers, respectively. The results pass the confirmation by numerical Milsteins method. The results show that when the noise intensity gradually increases, the tumor state changes from the weak persistence to the extinction, it demonstrates that the effect of stochastic perturbations on tumor cells is very prominent. In addition, by adjusting the value of <span><math><mrow><mi>a</mi><mrow><mo>(</mo><mi>n</mi><mi>P</mi><mo>)</mo></mrow></mrow></math></span> to simulate different medication doses, the results show that the killing rate of the medication to the tumor cells is the dominant factor in the long-term evolution of the tumor, and the bigger killing rate can lead to a rapid decrease in the number of tumor cells. Increasing the frequency of pulse therapy has also significant effects on tumor regression. The conclusion is consistent with the clinical observation of tumor treatment.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S100757042400515X/pdfft?md5=cd87ef3b8846d0c2ef258d324dfc6f44&pid=1-s2.0-S100757042400515X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical discretization of initial–boundary value problems for PDEs with integer and fractional order time derivatives","authors":"","doi":"10.1016/j.cnsns.2024.108331","DOIUrl":"10.1016/j.cnsns.2024.108331","url":null,"abstract":"<div><p>This paper is mainly concerned with introducing a numerical method for solving initial–boundary value problems with integer and fractional order time derivatives. The method is based on discretizing the considered problems with respect to spatial and temporal domains. With the help of finite difference methods, we transformed the studied problem into a set of fractional differential equations. Then, we implemented the fractional Adams method to solve this set in order to provide approximate solutions to the main problem. This combination results in an algorithm that can efficiently and accurately solve a general class of integer and fractional order initial–boundary value problems, such that it does not need to solve large systems of linear equations. In addition, we discussed the stability of the proposed scheme. Three illustrative examples are numerically solved to reveal the effectiveness and validity of the proposed technique.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005161/pdfft?md5=c32da0796500f9a40682bf5ad8d5719c&pid=1-s2.0-S1007570424005161-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalized scalar auxiliary variable approach for the Navier–Stokes-ω/Navier–Stokes-ω equations based on the grad-div stabilization","authors":"","doi":"10.1016/j.cnsns.2024.108329","DOIUrl":"10.1016/j.cnsns.2024.108329","url":null,"abstract":"<div><p>In this article, based on the grad-div stabilization, we propose a generalized scalar auxiliary variable approach for solving a fluid–fluid interaction problem governed by the Navier–Stokes-<span><math><mi>ω</mi></math></span>/Navier–Stokes-<span><math><mi>ω</mi></math></span> equations. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. The proposed scheme is almost unconditionally stable and requires solving only the linear equation with constant coefficient at each time step. It can also penalize for lack of mass conservation and improve the accuracy. Finally, a series of numerical experiments are carried out to illustrate the stability and effectiveness of the proposed scheme.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005148/pdfft?md5=e84604e57d5662b451f5f456ea102ca9&pid=1-s2.0-S1007570424005148-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Explicit exponential Runge–Kutta methods for semilinear time-fractional integro-differential equations","authors":"","doi":"10.1016/j.cnsns.2024.108332","DOIUrl":"10.1016/j.cnsns.2024.108332","url":null,"abstract":"<div><p>In this work, we consider and analyze explicit exponential Runge–Kutta methods for solving semilinear time-fractional integro-differential equation, which involves two nonlocal terms in time. Firstly, the temporal Runge–Kutta discretizations follow the idea of exponential integrators. Subsequently, we utilize the spectral Galerkin method to introduce a fully discrete scheme. Then, we mainly focus on discussing the one-stage and two-stage methods for solving the proposed semilinear problem. Based on special abstract settings, we perform the convergence analysis for the proposed two different stage methods. In this process, we heavily use estimates about the operator family <span><math><mrow><mo>{</mo><mover><mrow><mi>S</mi></mrow><mrow><mo>̃</mo></mrow></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>}</mo></mrow></math></span>, and in combination with Lipschitz continuous condition. Finally, some numerical experiments confirm theoretical results. Meanwhile, applying this scheme to the related linear problem yields high-order convergence, highlighting the advantages of explicit exponential Runge–Kutta methods.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005173/pdfft?md5=66d620e3c2a13d80a83205fe51950d69&pid=1-s2.0-S1007570424005173-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cascades of heterodimensional cycles via period doubling","authors":"","doi":"10.1016/j.cnsns.2024.108328","DOIUrl":"10.1016/j.cnsns.2024.108328","url":null,"abstract":"<div><p>A heterodimensional cycle is formed by the intersection of stable and unstable manifolds of two saddle periodic orbits that have unstable manifolds of different dimensions: connecting orbits exist from one periodic orbit to the other, and vice versa. The difference in dimensions of the invariant manifolds can only be achieved in vector fields of dimension at least four. At least one of the connecting orbits of the heterodimensional cycle will necessarily be structurally unstable, meaning that is does not persist under small perturbations. Nevertheless, the theory states that the existence of a heterodimensional cycle is generally a <em>robust</em> phenomenon: any sufficiently close vector field (in the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-topology) also has a heterodimensional cycle.</p><p>We investigate a particular four-dimensional vector field that is known to have a heterodimensional cycle. We continue this cycle as a codimension-one invariant set in a two-parameter plane. Our investigations make extensive use of advanced numerical methods that prove to be an important tool for uncovering the dynamics and providing insight into the underlying geometric structure. We study changes in the family of connecting orbits as two parameters vary and Floquet multipliers of the periodic orbits in the heterodimensional cycle change. In particular the Floquet multipliers of one of the periodic orbits change from real positive to real negative prior to a period-doubling bifurcation. We then focus on the transitions that occur near this period-doubling bifurcation and find that it generates new families of heterodimensional cycles with different geometric properties. Our careful numerical study suggests that further two-parameter continuation of the ‘period-doubled heterodimensional cycles’ gives rise to an abundance of heterodimensional cycles of different types in the limit of a period-doubling cascade.</p><p>Our results for this particular example vector field make a contribution to the emerging bifurcation theory of heterodimensional cycles. In particular, the bifurcation scenario we present can be viewed as a specific mechanism behind so-called stabilisation of a heterodimensional cycle via the embedding of one of its constituent periodic orbits into a more complex invariant set.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005136/pdfft?md5=f38edea7a0d479894640291d3ce40bfc&pid=1-s2.0-S1007570424005136-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142244139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unconditionally maximum principle-preserving linear method for a mass-conserved Allen–Cahn model with local Lagrange multiplier","authors":"","doi":"10.1016/j.cnsns.2024.108327","DOIUrl":"10.1016/j.cnsns.2024.108327","url":null,"abstract":"<div><p>In this work, we present a conservative Allen–Cahn (CAC) equation and investigate its unconditionally maximum principle-preserving linear numerical scheme. The operator splitting strategy is adopted to split the CAC model into a conventional AC equation and a mass correction equation. The standard finite difference method is used to discretize the equations in space. In the first step, the temporal discretization of the AC equation is performed by using the energy factorization technique. The discrete version of the maximum principle-preserving property for the AC equation is unconditionally satisfied. In the second step, we apply mass correction by using an explicit Euler-type approach. Without the constraint of time step, we estimate that the absolute value of the updated solution is bounded by 1. The unique solvability is analytically proved. In each time step, the proposed method is easy to implement because we only need to solve a linear elliptic type equation and then correct the solution in an explicit manner. Various computational experiments in two-dimensional and three-dimensional spaces are performed to confirm the performance of the proposed method. Moreover, the experiments also indicate that the proposed model can be used to simulate two-phase incompressible fluid flows.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142129764","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":"Finite time stability of nonlinear impulsive stochastic system and its application to neural networks","authors":"","doi":"10.1016/j.cnsns.2024.108298","DOIUrl":"10.1016/j.cnsns.2024.108298","url":null,"abstract":"<div><p>In this paper, we employ the Lyapunov theory to generalize the finite time stability (FTS) results from general deterministic impulsive systems to impulsive stochastic time-varying systems, which overcomes inherent challenges. Sufficient conditions for the FTS of the system under stabilizing and destabilizing impulses are established by using the method of average dwell interval (ADT). For FTS of stabilizing impulses, we relax the constraint on the differential operator by allowing it to be indefinite rather than strictly negative or semi-negative definite. Furthermore, the theoretical results are applied to impulsive stochastic neural networks. Finally, two numerical examples are given to validate the reliability and practicability of the obtained results.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142129768","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":"Simultaneous space–time Hermite wavelet method for time-fractional nonlinear weakly singular integro-partial differential equations","authors":"","doi":"10.1016/j.cnsns.2024.108324","DOIUrl":"10.1016/j.cnsns.2024.108324","url":null,"abstract":"<div><p>An innovative simultaneous space–time Hermite wavelet method has been developed to solve weakly singular fractional-order nonlinear integro-partial differential equations in one and two dimensions with a focus whose solutions are intermittent in both space and time. The proposed method is based on multi-dimensional Hermite wavelets and the quasilinearization technique. The simultaneous space–time approach does not fully exploit for time-fractional nonlinear weakly singular integro-partial differential equations. Subsequently, the convergence analysis is challenging when the solution depends on the entire time domain (including past and future time), and the governing equation is combined with Volterra and Fredholm integral operators. Considering these challenges, we use the quasilinearization technique to handle the nonlinearity of the problem and reconstruct it to a linear integro-partial differential equation with second-order accuracy. Then, we apply multi-dimensional Hermite wavelets as attractive candidates on the resulting linearized problems to effectively resolve the initial weak singularity at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>. In addition, the collocation method is used to determine the tensor-based wavelet coefficients within the decomposition domain. We elaborate on constructing the proposed simultaneous space–time Hermite wavelet method and design comprehensive algorithms for their implementation. Specifically, we emphasize the convergence analysis in the framework of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm and indicate high accuracy dependent on the regularity of the solution. The stability of the proposed wavelet-based numerical approximation is also discussed in the context of fractional-order nonlinear integro-partial differential equations involving both Volterra and Fredholm operators with weakly singular kernels. The proposed method is compared with existing methods available in the literature. Specifically, we highlighted its high accuracy and compared it with a recently developed hybrid numerical approach and finite difference methods. The efficiency and accuracy of the proposed method are demonstrated by solving several highly intermittent time-fractional nonlinear weakly singular integro-partial differential equations.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005094/pdfft?md5=02a1ddb04e33f46e3e9933ecc0361897&pid=1-s2.0-S1007570424005094-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}