Research on the conditions of reaction-diffusion equation occurring Hopf bifurcation under prescribed boundary condition

Author(s): Li Li

Reaction diffusion equation, which is well practically applied at present, is a good model to describe the natural phenomenon. Although Hopf bifurcation is easy, it is vitally important as a dynamic bifurcation. Hopf bifurcation theory has been the essential method to analyze the appearance and disappearance of the small amplitude periodic solution of the differential equation, mainly because its research theory and numerical research method are significant for the dynamic bifurcation and limit cycle. Moreover, there is inseparable relationship between Hopf bifurcation and the theory of self-excited vibration, so Hopf bifurcation is widely used in the modern engineering. First of all, this research elaborates the research status and significance of reaction diffusion equation. Then, the paper explains reaction diffusion equation and discusses its equilibrium, distribution and linear stability. In the end, the research discusses the conditions of one dimension reaction equation occurring Hopf bifurcation and analyzes the stability and conditions. Through the study of the whole process, it can be seen that reaction diffusion equation can be widely applied. Therefore, it is important for describing the natural movements and involves a number of disciplines. Furthermore, many mathematical models can be switched into reaction diffusion equation so that it is more beneficial for research. The research on one dimension reaction diffusion equation will be useful for the analysis and awareness of several natural phenomena.

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