Advances in continuous and discrete models最新文献

A q-analogue for partial-fraction decomposition of a rational function and its application 有理函数偏分分解的 q 类比及其应用

Advances in continuous and discrete models Pub Date : 2024-06-12 DOI: 10.1186/s13662-024-03814-7

Ze-Qian Luo, Qiu-Ming Luo

引用次数: 0

A pair of centro-symmetric heteroclinic orbits coined 一对中心对称的异质轨道被称为

Advances in continuous and discrete models Pub Date : 2024-05-22 DOI: 10.1186/s13662-024-03809-4

Haijun Wang, Jun Pan, Guiyao Ke, Feiyu Hu

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The impact of resource limitation on the pest-natural enemy ecosystem with anti-predator behavior and fear effect 资源限制对害虫-天敌生态系统的影响与反捕食行为和恐惧效应

Advances in continuous and discrete models Pub Date : 2024-04-24 DOI: 10.1186/s13662-024-03804-9

Wenjie Qin, Zhengjun Dong

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Conservative Fourier spectral method for a class of modified Zakharov system with high-order space fractional quantum correction 一类具有高阶空间分数量子校正的修正Zakharov系统的保守傅里叶谱方法

Advances in continuous and discrete models Pub Date : 2023-11-03 DOI: 10.1186/s13662-023-03790-4

Tao Guo, Aiguo Xiao, Junjie Wang, Xueyang Li

引用次数: 0

Adaptive neural-domain refinement for solving time-dependent differential equations 求解时变微分方程的自适应神经域细化

Advances in continuous and discrete models Pub Date : 2023-10-25 DOI: 10.1186/s13662-023-03789-x

Toni Schneidereit, Michael Breuß

{"title":"Adaptive neural-domain refinement for solving time-dependent differential equations","authors":"Toni Schneidereit, Michael Breuß","doi":"10.1186/s13662-023-03789-x","DOIUrl":"https://doi.org/10.1186/s13662-023-03789-x","url":null,"abstract":"Abstract A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent differential equations, one can apply the recently developed method of domain segmentation. That is, the domain may be split into several subdomains, on which the optimisation problem is solved. In classic adaptive numerical methods, the mesh as well as the domain may be refined or decomposed, in order to improve the accuracy. Also, the degree of approximation accuracy may be adapted. Therefore, it is desirable to transfer such important and successful strategies to the field of neural-network-based solutions. In the presented work, we propose a novel adaptive neural approach to meet this aim for solving time-dependent problems. To this end, each subdomain is reduced in size until the optimisation is resolved up to a predefined training accuracy. In addition, while the neural networks employed are by default small, we propose a means to adjust also the number of neurons in an adaptive way. We introduce conditions to automatically confirm the solution reliability and optimise computational parameters whenever it is necessary. Results are provided for several initial-value problems that illustrate important computational properties of the method.","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Universal approximation property of a continuous neural network based on a nonlinear diffusion equation 基于非线性扩散方程的连续神经网络的普遍逼近性质

Advances in continuous and discrete models Pub Date : 2023-10-25 DOI: 10.1186/s13662-023-03787-z

Hirotada Honda

引用次数: 0

Bifurcation and chaos in a discrete Holling–Tanner model with Beddington–DeAngelis functional response 具有Beddington-DeAngelis函数响应的离散Holling-Tanner模型的分岔和混沌

Advances in continuous and discrete models Pub Date : 2023-10-23 DOI: 10.1186/s13662-023-03788-y

Run Yang, Jianglin Zhao

引用次数: 0

Stability and dynamics of a stochastic discrete fractional-order chaotic system with short memory 具有短记忆的随机离散分数阶混沌系统的稳定性和动力学

Advances in continuous and discrete models Pub Date : 2023-10-10 DOI: 10.1186/s13662-023-03786-0

Jie Ran, Jixiu Qiu, Yonghui Zhou

引用次数: 0

Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM BSLM内共享特征曲线耦合Burgers方程的算法

Advances in continuous and discrete models Pub Date : 2023-10-09 DOI: 10.1186/s13662-023-03785-1

Soyoon Bak, Yonghyeon Jeon

引用次数: 0

Forward invariant set preservation in discrete dynamical systems and numerical schemes for ODEs: application in biosciences 离散动力系统的前向不变量集保持和ode的数值格式:在生物科学中的应用

Advances in continuous and discrete models Pub Date : 2023-09-22 DOI: 10.1186/s13662-023-03784-2

Roumen Anguelov, Jean M.-S. Lubuma

{"title":"Forward invariant set preservation in discrete dynamical systems and numerical schemes for ODEs: application in biosciences","authors":"Roumen Anguelov, Jean M.-S. Lubuma","doi":"10.1186/s13662-023-03784-2","DOIUrl":"https://doi.org/10.1186/s13662-023-03784-2","url":null,"abstract":"Abstract We present two results on the analysis of discrete dynamical systems and finite difference discretizations of continuous dynamical systems, which preserve their dynamics and essential properties. The first result provides a sufficient condition for forward invariance of a set under discrete dynamical systems of specific type, namely time-reversible ones. The condition involves only the boundary of the set. It is a discrete analog of the widely used tangent condition for continuous systems ( viz. the vector field points either inwards or is tangent to the boundary of the set). The second result is nonstandard finite difference (NSFD) scheme for dynamical systems defined by systems of ordinary differential equations. The NSFD scheme preserves the hyperbolic equilibria of the continuous system as well as their stability. Further, the scheme is time reversible and, through the first result, inherits from the continuous model the forward invariance of the domain. We show that the scheme is of second order, thereby solving a pending problem on the construction of higher-order nonstandard schemes without spurious solutions. It is shown that the new scheme applies directly for mass action-based models of biological and chemical processes. The application of these results, including some numerical simulations for invariant sets, is exemplified on a general Susceptible-Infective-Recovered/Removed (SIR)-type epidemiological model, which may have arbitrary large number of infective or recovered/removed compartments.","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0