Hopf bifurcation of a tumor immune model with time delay

Abstract

In this paper, a tumor immune model with time delay is studied. First, the stability of nonnegative equilibria is analyzed. Then the time delay τ is selected as a bifurcation parameter and the existence of Hopf bifurcation is proved. Finally, by using the canonical method and the central manifold theory, the criteria for judging the direction and stability of Hopf bifurcation are given.

Key words： Tumor immune model; time delay; Hopf bifurcation; existence; direction; stability

References

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