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A Hybrid Approach For Synchronizing Between Two Reaction–Diffusion Systems Of Integer- And Fractional-Order Applied On Certain Chemical Models

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  • BO WANG

    (School of Electronic Information and Automation, Aba Teachers University, Wenchuan 623002, China2School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu 610054, China)

  • ADEL OUANNAS

    (Department of Mathematics and Computer Science, University of Larbi Ben Mhidi, Oum El Bouaghi 04000, Algeria)

  • YELIZ KARACA

    (University of Massachusetts Medical School (UMASS), Worcester, MA 01655, USA)

  • WEI-FENG XIA

    (School of Engineering, Huzhou University, Huzhou 313000, P. R. China6Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China)

  • HADI JAHANSHAHI

    (Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada R3T 5V6, Canada)

  • ABDULHAMEED F. ALKHATEEB

    (Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia)

  • MAJID NOUR

    (Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia)

Abstract

In this study, a synchronization problem for spatio-temporal partial differential systems is addressed and researched within a subjectivist framework. In light of Lyapunov direct method and some proposed nonlinear controllers, a new scheme is established to accomplish a full synchronization between two reaction–diffusion systems of integer- and fractional-order. In particular, a novel vector-valued control law is analytically derived to attain the desired synchronization between two chemical models, namely, the Lengyel–Epstein and Gray–Scott models. To validate the obtained theoretical results, further numerical simulations are carried out in 2D and 3D configurations.

Suggested Citation

  • Bo Wang & Adel Ouannas & Yeliz Karaca & Wei-Feng Xia & Hadi Jahanshahi & Abdulhameed F. Alkhateeb & Majid Nour, 2022. "A Hybrid Approach For Synchronizing Between Two Reaction–Diffusion Systems Of Integer- And Fractional-Order Applied On Certain Chemical Models," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-11, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401454
    DOI: 10.1142/S0218348X22401454
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