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Dynamic Properties of a Forest Fire Model

Author

Listed:
  • Na Min
  • Hongyang Zhang
  • Zhilin Qu

Abstract

The reaction‐diffusion equations have been widely used in physics, chemistry, and other areas. Forest fire can also be described by such equations. We here propose a fighting forest fire model. By using the normal form approach theory and center manifold theory, we analyze the stability of the trivial solution and Hopf bifurcation of this model. Finally, we give the numerical simulations to illustrate the effectiveness of our results.

Suggested Citation

  • Na Min & Hongyang Zhang & Zhilin Qu, 2012. "Dynamic Properties of a Forest Fire Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:948480
    DOI: 10.1155/2012/948480
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    References listed on IDEAS

    as
    1. Hongyang Zhang & Chunrui Zhang, 2012. "Dynamic Properties of a Differential‐Algebraic Biological Economic System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Honecker, A. & Peschel, I., 1997. "Length scales and power laws in the two-dimensional forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 239(4), pages 509-530.
    3. Hongyang Zhang & Chunrui Zhang, 2012. "Dynamic Properties of a Differential-Algebraic Biological Economic System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, January.
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    Cited by:

    1. Weifang Yan & Rui Liu, 2013. "Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time‐Delayed Degenerate Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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