Fractal and Fractional最新文献_第2页

Iterative Learning Formation Control via Input Sharing for Fractional-Order Singular Multi-Agent Systems with Local Lipschitz Nonlinearity 通过输入共享对具有局部 Lipschitz 非线性的分数阶奇异多代理系统进行迭代学习编队控制

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-11 DOI: 10.3390/fractalfract8060347

Guangxu Wang, Rui Wang, Danhu Yi, Xingyu Zhou, Shuyu Zhang

引用次数: 0

Common Attractors for Generalized F-Iterated Function Systems in G-Metric Spaces G度量空间中广义F迭代函数系统的共同吸引子

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-10 DOI: 10.3390/fractalfract8060346

T. Nazir, Sergei Silvestrov

引用次数: 0

Fractal Tent Map with Application to Surrogate Testing 分形帐篷图在替代测试中的应用

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-07 DOI: 10.3390/fractalfract8060344

E. Kopets, V. Rybin, Oleg Vasilchenko, D. Butusov, Petr Fedoseev, Artur Karimov

{"title":"Fractal Tent Map with Application to Surrogate Testing","authors":"E. Kopets, V. Rybin, Oleg Vasilchenko, D. Butusov, Petr Fedoseev, Artur Karimov","doi":"10.3390/fractalfract8060344","DOIUrl":"https://doi.org/10.3390/fractalfract8060344","url":null,"abstract":"Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141375290","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}

引用次数: 0

Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels 指数核分式积分的进一步赫米特-哈达马德式不等式

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-07 DOI: 10.3390/fractalfract8060345

Hong Li, B. Meftah, Wedad Saleh, Hongyan Xu, A. Kiliçman, A. Lakhdari

引用次数: 0

A Dynamical Analysis and New Traveling Wave Solution of the Fractional Coupled Konopelchenko–Dubrovsky Model 分数耦合科诺佩琴科-杜布罗夫斯基模型的动力学分析和新的行波解法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-06 DOI: 10.3390/fractalfract8060341

Jin Wang, Zhao Li

引用次数: 0

Well-Posedness and Hyers–Ulam Stability of Fractional Stochastic Delay Systems Governed by the Rosenblatt Process 罗森布拉特过程控制的分数随机延迟系统的良好假设性和海尔-乌兰稳定性

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-06 DOI: 10.3390/fractalfract8060342

Ghada AlNemer, Mohamed Hosny, R. Udhayakumar, Ahmed M. Elshenhab

引用次数: 0

Quantized Nonfragile State Estimation of Memristor-Based Fractional-Order Neural Networks with Hybrid Time Delays Subject to Sensor Saturations 受传感器饱和影响的基于 Memristor 的具有混合时间延迟的分数阶神经网络的量化非脆弱状态估计

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-06 DOI: 10.3390/fractalfract8060343

Xiaoguang Shao, Yanjuan Lu, Jie Zhang, Ming Lyu, Yu Yang

引用次数: 0

Day of the Week Effect on the World Exchange Rates through Fractal Analysis 通过分形分析看星期对世界汇率的影响

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-06 DOI: 10.3390/fractalfract8060340

Werner D. Kristjanpoller, Benjamin Miranda Tabak

引用次数: 0

Command Filter-Based Adaptive Neural Control for Nonstrict-Feedback Nonlinear Systems with Prescribed Performance 基于指令滤波器的自适应神经控制，用于具有规定性能的非严格反馈非线性系统

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-05 DOI: 10.3390/fractalfract8060339

Xiaoli Yang, Jing Li, S. Ge, Xiaoling Liang, Tao Han

{"title":"Command Filter-Based Adaptive Neural Control for Nonstrict-Feedback Nonlinear Systems with Prescribed Performance","authors":"Xiaoli Yang, Jing Li, S. Ge, Xiaoling Liang, Tao Han","doi":"10.3390/fractalfract8060339","DOIUrl":"https://doi.org/10.3390/fractalfract8060339","url":null,"abstract":"In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new performance function, the fixed-time performance function, which does not depend on the accurate initial value of the error signal and has the ability of fixed-time convergence, is proposed for the first time. A radial basis function neural network is introduced to identify unknown nonlinear functions, and the characteristic of Gaussian basis functions is utilized to overcome the difficulties of the nonstrict-feedback structure. Moreover, in contrast to the traditional Backstepping technique, a command filter-based adaptive control algorithm is constructed, which solves the “explosion of complexity” problem and relaxes the assumption on the reference signal. Additionally, it is guaranteed that the tracking error falls within a prescribed small neighborhood by the designed performance functions in fixed time, and the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the proposed control scheme is verified by numerical simulation.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141384939","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}

引用次数: 0

Nonlocal Changing-Sign Perturbation Tempered Fractional Sub-Diffusion Model with Weak Singularity 具有弱奇异性的非局部变号扰动节制分形次扩散模型

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-05 DOI: 10.3390/fractalfract8060337

Xinguang Zhang, Jingsong Chen, Peng Chen, Lishuang Li, Yonghong Wu

引用次数: 0