Abstract
In this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is proven that TNF model undergoes codimension-1 bifurcation, while Hopf bifurcation does not occur in the non-delay model. For delayed TNF, we take into the late response of fat cells to tumor cells. Consequently, the delay factor is a considerable parameter in TNF model. Hence, we presented a formula of the time delay value for the occurrence of periodic solutions. Additionally, the stability of Hopf bifurcation was analysed. Numerical simulations are provided to illustrate and extend the theoretical results, we provide our study with numerical simulations inclusive families of periodic solutions.