Fractional-Order Degn–Harrison Reaction–Diffusion Model: Finite-Time Dynamics of Stability and Synchronization

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Computation Pub Date : 2024-07-12 DOI:10.3390/computation12070144

Ma'mon Abu Hammad, Issam Bendib, W. Alshanti, Ahmad Alshanty, Adel Ouannas, Amel Hioual, S. Momani

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Abstract

This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criteria, this lemma represents a significant extension of prior findings, laying the groundwork for subsequent investigations. Building upon this foundation, we proceed to develop efficient dependent linear controllers designed to orchestrate finite-time synchronization. Leveraging the power of a Lyapunov function, we derive new, robust conditions that ensure the attainment of synchronization within a predefined time frame. This innovative approach not only enhances our understanding of finite-time synchronization, but also offers practical solutions for its realization in complex systems. To validate the efficacy and applicability of our proposed methodology, extensive numerical simulations are conducted. Through this comprehensive analysis, we aim to contribute valuable insights to the field of fractional-order reaction–diffusion systems while paving the way for practical implementations in real-world applications.

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分数阶 Degn-Harrison 反应扩散模型：稳定性和同步性的有限时间动力学

本研究旨在探讨分数阶 Degn-Harrison 反应扩散系统特定子集中的有限时间同步问题。为了实现这一目标，我们首先引入了一个专门用于有限时间稳定性分析的新式lemma。与现有标准不同的是，该 Lemma 是对先前研究成果的重大扩展，为后续研究奠定了基础。在此基础上，我们着手开发高效的依赖线性控制器，以协调有限时间同步。利用 Lyapunov 函数的强大功能，我们推导出新的稳健条件，确保在预定的时间框架内实现同步。这种创新方法不仅增强了我们对有限时间同步的理解，还为在复杂系统中实现有限时间同步提供了切实可行的解决方案。为了验证我们提出的方法的有效性和适用性，我们进行了大量的数值模拟。通过这一全面分析，我们旨在为分数阶反应扩散系统领域贡献有价值的见解，同时为在现实世界中的实际应用铺平道路。

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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.