Special Session 13: Nonlinear differential and difference equations with applications to population dynamics

Bifurcations of co-dimension two in a model of immune and neoplasia for two ODEs

Eymard Hernandez-Lopez
UAGro-TESOEM
Mexico
Co-Author(s):    Joaquin Delgado, Lucia Ivonne Hernandez Martinez
Abstract:
In this talk, we present a dynamic model between cancer cells and lymphocytes and a description of their dynamics, such as the existence of saddle-node and Takens-Bogdanov bifurcations and that there are no degenerated Takens-Bogdanov bifurcations in the five-parameter two ODEs system. Furthermore, we present our contribution to this system through a two-dimensional bifurcation diagram, such as the generalized Andronov-Hopf bifurcation, also known as the Bautin bifurcation. Also, we complete the diagram of codimension two, at the same time, heteroclinic and homoclinic orbits.