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

• DOI: 10.3390/computation12070144
• Publication Date: 2024-07-12T12:47:41Z
• Authors: Ma’mon Abu Hammad; Issam Bendib; Waseem Ghazi Alsh...; Ahmad Alshanty; Adel Ouannas; Amel Hioual; Shaher Momani
• Keywords: finite-time synchronization; Computer Networks and Communications; Economics; Synchronization; 01 natural sciences; Mathematical analysis; Diffusion; Dynamics of Synchronization in Complex Networks; Degn–Harrison reaction–diffusion systems; 0103 physical sciences; Synchronization (alternating current); Machine learning; finite-time stability; FOS: Mathematics; Stability (learning theory); Anomalous Diffusion Modeling and Analysis; Order (exchange); Topology (electrical circuits); Lyapunov function; Time-Fractional Diffusion Equation; Physics; Statistical and Nonlinear Physics; QA75.5-76.95; Acoustics; Applied mathematics; Computer science; Fractional Derivatives; Physics and Astronomy; Reaction–diffusion system; Combinatorics; Electronic computers. Computer science; Modeling and Simulation; Stochastic Resonance in Nonlinear Systems; Computer Science; Physical Sciences; Thermodynamics; Fractional Calculus; Statistical physics; Reaction-Diffusion Model; Mathematics; Dynamics (music); Finance

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.