Abstract
The general Brusselator system is considered under homogeneous Neumann boundary conditions. The existence results of the Hopf bifurcation to the ordinary differential equation (ODE) and partial differential equation (PDE) models are obtained. By the center manifold theory and the normal form method, the bifurcation direction and stability of periodic solutions are established. Moreover, some numerical simulations are shown to support the analytical results. At the same time, the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.
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Project supported by the National Natural Science Foundation of China (Nos. 10971124 and 11001160), the Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2011JQ1015 and 2009JQ100), and the Doctor Start-up Research Fund of Shaanxi University of Science and Technology (No. BJ10-17)
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Guo, Gh., Wu, Jh. & Ren, Xh. Hopf bifurcation in general Brusselator system with diffusion. Appl. Math. Mech.-Engl. Ed. 32, 1177–1186 (2011). https://doi.org/10.1007/s10483-011-1491-6
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DOI: https://doi.org/10.1007/s10483-011-1491-6