Pattern Formation in a Reaction–Diffusion System with Time-Fractional Derivatives

被引：0
|
作者：
Zenyuk D.A. [1 ]
Malinetsky G.G. [1 ]
机构：
[1] Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow
来源：
Mathematical Models and Computer Simulations | 2021年 / 13卷 / 1期
关键词：
fractional calculus; reaction–diffusion systems;
D O I：
10.1134/S2070048221010178
中图分类号：
学科分类号：
摘要：
Abstract: In this paper possible scenarios of pattern formation in nonlinear media with diffusion and differential operators of a noninteger order are studied for the abstract Brusselator model. Through the standard linear analysis exact critical values for different types of instabilities are derived. It is shown that the stability criteria significantly depend on the order of the fractional derivative in the case of the Hopf and C2TH bifurcations. Predictions of the linear theory are confirmed by the numerical simulation. © 2021, Pleiades Publishing, Ltd.
引用
收藏
页码：126 / 133
页数：7
相关论文
共 50 条
  • [1] Pattern formation in a fractional reaction-diffusion system
    Gafiychuk, V. V.
    Datsko, B. Yo.
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2006, 365 (02) : 300 - 306
  • [2] A class of time-fractional diffusion equations with generalized fractional derivatives
    Alikhanov, Anatoly A.
    Huang, Chengming
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 414
  • [3] On the solutions of coupled nonlinear time-fractional diffusion-reaction system with time delays
    Priyendhu, K. S.
    Prakash, P.
    Lakshmanan, M.
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2024,
  • [4] ON THE CRITICAL BEHAVIOR FOR TIME-FRACTIONAL REACTION DIFFUSION PROBLEMS
    Aldawish, Ibtisam
    Samet, Bessem
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (08): : 2030 - 2046
  • [5] On the solutions of time-fractional reaction-diffusion equations
    Rida, S. Z.
    El-Sayed, A. M. A.
    Arafa, A. A. M.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (12) : 3847 - 3854
  • [6] AN INVERSE PROBLEM OF IDENTIFYING TWO COEFFICIENTS IN A TIME-FRACTIONAL REACTION DIFFUSION SYSTEM
    Srati, Mohammed
    Oulmelk, Abdessamad
    Afraites, Lekbir
    Hadri, Aissam
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023,
  • [7] Computational Scheme for the Time-Fractional Reaction–Diffusion Brusselator Model
    Alquran M.
    Jaradat I.
    Ali M.
    Abu Aljazar A.
    [J]. International Journal of Applied and Computational Mathematics, 2020, 6 (5)
  • [8] NUMERICAL APPROACH TO THE TIME-FRACTIONAL REACTION-DIFFUSION EQUATION
    Qiu, Yu-Yang
    [J]. THERMAL SCIENCE, 2019, 23 (04): : 2245 - 2251
  • [9] Numerical simulation for time-fractional nonlinear reaction-diffusion system on a uniform and nonuniform time stepping
    Zahra, Waheed K.
    Hikal, Manal M.
    Baleanu, Dumitru
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (07) : 5340 - 5364
  • [10] Stabilization and uncertainty analysis of a time-fractional reaction diffusion equation cascaded with a time-fractional hyperbolic partial differential equation
    Chen, Juan
    Zhuang, Bo
    Tepljakov, Aleksei
    Petlenkov, Eduard
    [J]. ASIAN JOURNAL OF CONTROL, 2022, 24 (05) : 2294 - 2310
12345