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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Hopf Bifurcation in a Delayed Brusselator Model with Network Structure

Journal of Applied Nonlinear Dynamics 11(4) (2022) 895--912 | DOI:10.5890/JAND.2022.12.009

Hongxia Liu, Ranchao Wu, Mengxin Chen

School of Mathematical Sciences, Anhui University, Hefei, 230601, China

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Abstract

In this paper, the Brusselator reactor model with time delay and network structure is introduced and investigated. In view of understanding spatiotemporal dynamics of the model, dynamical analysis about the reactor is first carried out, such as stability and bifurcation analysis near the homogeneous steady state via choosing time delay as the critical parameter. It is found that time delay can induce stable and unstable states of the homogeneous steady state, and the model experiences the Hopf bifurcation at such critical value. Then the center manifold reduction and the normal form theory are applied to explore the detailed properties of the Hopf bifurcation. It is noted that such Brusselator model possesses the supercritical and subcritical Hopf bifurcation. Numerical simulations are performed to verify the validity of theoretical analysis.

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