Abstract

The article mainly researched the Hopf bifurcation of Lorenz-like system about the coefficient of the quadratic term. When the quadratic term changes, the solution to the Lorenz-like system will become the local periodic solution. Further the stability of this periodic solution and the bifurcation direction of this periodic solution were discussed, and found when the quadratic term comes through a threshold , the direction of hopf bifurcation and stability were given, and the result as follows. If , when , the direction of bifurcation is , when , the direction of bifurcation is ; (b) if , we have the contrary result. That is when , the direction of bifurcation is ; when , the direction of bifurcation is . If , the bifurcation solution is asymptotically stable; if , the bifurcation solution is not asymptotically stable. Finally employing the matlab compute the numerical periodic solution, the results fit the theory well.

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