Hopf bifurcations in general systems of Brusselator type |
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| Affiliation: | 1. Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, Brazil;2. Grupo de Física da Matéria Condensada, Núcleo de Ciencias Exatas - NCEx, Campus Arapiraca, Universidade Federal de Alagoas, 53309-005 Arapiraca-AL, Brazil;3. Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA;4. International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil;1. Department of Mathematics, Shanghai Normal University, Shanghai 200235, China;2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
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| Abstract: | This paper is concerned with general models of Brusselator type subject to the homogeneous Neumann boundary condition. The existence of Hopf bifurcation for the ODE and PDE models is obtained. By the center manifold theory and the normal form method, the bifurcation direction and stability of bifurcating periodic solutions are established. Moreover, some numerical simulations are shown to support the analytical results. |
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| Keywords: | Brusselator type Hopf bifurcation Center manifold Normal form |
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