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Hopf bifurcation analysis of a reaction-diffusion Sel'kov system |
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| Authors: | Wei Han Zhenhua Bao |
| Institution: | a Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China b School of Mathematical Sciences, Fudan University, Shanghai 200433, China c School of Mathematics, Liaoning Normal University, Dalian 116029, China |
| Abstract: | A reaction-diffusion system known as the Sel'kov model subject to the homogeneous Neumann boundary condition is investigated, where detailed Hopf bifurcation analysis is performed. We not only show the existence of the spatially homogeneous/non-homogeneous periodic solutions of the system, but also derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution. |
| Keywords: | Reaction-diffusion Sel'kov system Hopf bifurcation Spatial homogeneous/non-homogeneous periodic orbits Stability |
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