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Volume 5, Issue 3
Analysis of Dynamic Properties of Forest Beetle Outbreak Model

Xuetian Zhang & Chunrui Zhang

DOI: 10.12150/jnma.2023.580

J. Nonl. Mod. Anal., 5 (2023), pp. 580-596.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Reaction-diffusion equation, Turing instability, Hopf bifurcation, Turing-Hopf bifurcation.

  • AMS Subject Headings

34C23, 35K57

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-580, author = {Zhang , Xuetian and Zhang , Chunrui}, title = {Analysis of Dynamic Properties of Forest Beetle Outbreak Model}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {580--596}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.580}, url = {http://global-sci.org/intro/article_detail/jnma/21953.html} }
TY - JOUR T1 - Analysis of Dynamic Properties of Forest Beetle Outbreak Model AU - Zhang , Xuetian AU - Zhang , Chunrui JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 580 EP - 596 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.580 UR - https://global-sci.org/intro/article_detail/jnma/21953.html KW - Reaction-diffusion equation, Turing instability, Hopf bifurcation, Turing-Hopf bifurcation. AB -

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.

Xuetian Zhang & Chunrui Zhang. (2023). Analysis of Dynamic Properties of Forest Beetle Outbreak Model. Journal of Nonlinear Modeling and Analysis. 5 (3). 580-596. doi:10.12150/jnma.2023.580
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