Phase transitions in tumor growth: III vascular and metastasis behavior

We propose a mechanism for avascular, vascular and metastasis tumor growth based on a chemical network model. Vascular growth and metastasis, appear as a hard phase transition type, as “first order”, through a supercritical Andronov-Hopf bifurcation, emergence of limit cycle and then through a cascade of bifurcations type saddle-foci Shilnikov's bifurcation. Finally, the thermodynamics framework developed shows that the entropy production rate, as a Lyapunov function, indicates the directional character and stability of the dynamical behavior of tumor growth according to this model.