Cross-diffusion induced Turing instability of Hopf bifurcating periodic solutions in the reaction-diffusion enzyme reaction model

被引：2

作者：

Liu, Haicheng ^{[1
]}

Yuan, Wenshuo ^{[1
]}

Ge, Bin ^{[1
]}

Shen, Jihong ^{[1
]}

机构：

[1] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Heilongjiang, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2024年 / 17卷 / 04期

关键词：

Sporns-Seelig model; diffusion; Hopf bifurcation; periodic solutions; Turing instability; LENGYEL-EPSTEIN SYSTEM; PREDATOR-PREY SYSTEM; CELLULAR CONTROL-MODELS; PATTERN-FORMATION; SPATIOTEMPORAL PATTERNS; NEGATIVE FEEDBACK; BEHAVIOR; DELAYS;

D O I：

10.1142/S1793524523500365

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Aiming at the spatial pattern phenomenon in biochemical reactions, an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study object. Applying the central manifold theory, normal form method, local Hopf bifurcation theorem and perturbation theory, we study Turing instability of the spatially homogeneous Hopf bifurcation periodic solutions. At last, the theoretical results are verified by numerical simulations.

引用

页数：18

共 50 条

[1] Turing instability of the periodic solutions for reaction-diffusion systems with cross-diffusion and the patch model with cross-diffusion-like coupling
Yi, Fengqi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 281 : 379 - 410
[2] Turing instability of periodic solutions for a general Brusselator model with cross-diffusion
Guo, Gaihui
Wei, Tingting
Jia, Fujie
Abbakar, Khalid Ahmed
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 541 (01)
[3] Instability induced by cross-diffusion in reaction-diffusion systems
Tian, Canrong
Lin, Zhigui
Pedersen, Michael
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (02) : 1036 - 1045
[4] Turing instability and traveling fronts for a nonlinear reaction-diffusion system with cross-diffusion
Gambino, G.
Lombardo, M. C.
Sammartino, M.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2012, 82 (06) : 1112 - 1132
[5] CROSS-DIFFUSION INDUCED INSTABILITY AND STABILITY IN REACTION-DIFFUSION SYSTEMS
Shi, Junping
Xie, Zhifu
Little, Kristina
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2011, 1 (01): : 95 - 119
[6] Turing instability of the periodic solutions for a predator-prey model with Allee effect and cross-diffusion
Yang, Hong
Zhong, Zhaoman
ADVANCES IN CONTINUOUS AND DISCRETE MODELS, 2025, 2025 (01):
[7] Turing Instability of Periodic Solutions for a General Degn-Harrison Model with Cross-Diffusion
Guo, Gaihui
Li, Wangrui
Du, Yanfei
Jafari, Sajad
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (02)
[8] Turing Instability of Spatially Homogeneous Periodic Solutions in a Reaction-Diffusion Bimolecular Model
Yan, Xiang-Ping
Lian, Li-Na
Zhang, Cun-Hua
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025,
[9] Dynamics for a Charge Transfer Model with Cross-Diffusion: Turing Instability of Periodic Solutions
Guo, Gaihui
You, Jing
Du, Xinhuan
Li, Yanling
ACTA APPLICANDAE MATHEMATICAE, 2024, 192 (01)
[10] Turing Instability and Pattern Induced by Cross-Diffusion for a Nonlinear Reaction-Diffusion System of Turbulence-Shear Flow Interaction
周辉
彭亚红
Journal of Donghua University(English Edition), 2017, 34 (05) : 689 - 693

← 1 2 3 4 5 →