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We consider a delay differential equation that occurs in the study of chronicmyelogenous leukemia. After shortly reminding some previous results concerningthe stability of equilibrium solutions, we concentrate on the study ofstability of periodic solutions emerged by Hopf bifurcation from a certainequilibrium point. We give the algorithm for approximating a center manifold ata typical point (in the parameter space) of Hopf bifurcation (and an unstablemanifold in the vicinity of such a point, where such a manifold exists). Thenwe find the normal form of the equation restricted to the center manifold, bycomputing the first Lyapunov coefficient. The normal form allows us toestablish the stability properties of the periodic solutions occurred by Hopfbifurcation.

Stability of equilibrium and periodic solutions of a delay equation modeling leukemia