News & Announcements
Links
Analysis of Dynamic Properties of Forest Beetle Outbreak Model
  
View Full Text  View/Add Comment  Download reader
KeyWord:Reaction-diffusion equation, Turing instability, Hopf bifurcation, Turing-Hopf bifurcation
Author NameAffiliation
Xuetian Zhang Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China 
Chunrui Zhang Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China 
Hits: 155
Download times: 251
Abstract:
      This paper mainly studies the dynamic properties of the forest beetle outbreak model. The existence of the positive equilibrium point and the local stability of the positive equilibrium point of the system are analyzed, and the relevant conclusions are drawn. After that, the existence of Turing instability, Hopf bifurcation and Turing-Hopf bifurcation are discussed respectively, and the necessary conditions for existence are given. Finally, the normal form of the Turing-Hopf point is calculated, and some dynamic properties at the point are analyzed by numerical simulation.