The Forest Fire Model And Its Application

The forest fire is the most active in impact factors of forest ecosystem. Currently, how to reduce the extent of forest fires’ harm is a hot issue, how to predict forest fire accurately and save fire rapidly are the most direct methods which cut the extent of fire harm. Building mathematical model of forest fire is an important approach with which people can study the occurrence of forest fires and forest fire. And it can provide the academic support for the forest fire.This article built a new mathematical model of forest fire with several factors such as the spread of firefighters in fire, resurgence chance of the extinguished forest fire and natural factors, And it analyzed the system’s dynamic properties such as the stability of equilibrium point and Hopf bifurcation. Finally, it made numerical simulations whose results proved conclusions.This article has mainly following conclusions.Theorem1(1) If α≥1, the equilibrium point is global asymptotic stability.(2) If α <1and (1-a)/c≤b≤1/(ac+c), the equilibrium point is global asymptotic stability.Theorem2(1) The sign of μ2determines the direction of Hopf bifurcation. When μ2>0, the Hopf bifurcation is supercritical, when μ2<0, the Hopf bifurcation is subcritical.(2) The sign of β2determines the stability of bifurcated periodic solutions.When β2<0,periodic solutions are stable, when β>0, periodic solutions are unstable。(3) The sign of T2determines the period of bifurcated periodic solutions. When T2<0, the period increases, when T2>0, the period decreases.