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Diffusion‐driven codimension‐2 Turing–Hopf bifurcation in the general Brusselator model
Author(s) -
Kong Lei,
Zhu Changrong
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7504
Subject(s) - brusselator , mathematics , hopf bifurcation , center manifold , codimension , neumann boundary condition , mathematical analysis , biological applications of bifurcation theory , reaction–diffusion system , degenerate energy levels , bifurcation theory , bifurcation , boundary (topology) , nonlinear system , physics , quantum mechanics
In this paper, spatiotemporal dynamics for a general reaction–diffusion system of Brusselator type under the homogeneous Neumann boundary condition is considered. It is shownthat the reaction–diffusion system has a unique steady state solution. For some suitable parameters, we prove that the steady state solution can be a codimension‐2 Turing–Hopf point. To understand the spatiotemporal dynamics in the vicinity of the Turing–Hopf bifurcation point, we calculate and analyze the normal form on the center manifold by analytical methods. A wealth of complex spatiotemporal dynamics near the degenerate point are obtained. It is proved that the system undergoes a codimension‐2 Turing–Hopf bifurcation. Moreover, several numerical simulations are carried out to illustrate the validity of our theoretical results.