Bifurcation Analysis in a Cancer Growth Model

Abstract

A mathematical model describing interactions among tumor cells, healthy host cells and immune cells is extensively investigated through bifurcation analysis with all parameters fixed except one bifurcation parameter. Transcritical bifurcation and saddle-node bifurcation are studied in the vector fields restricted to the corresponding center manifolds. Hopf bifurcation is analyzed in the frequency domain. In particular, the sixth-order harmonic balance approximations to the frequency and the amplitude of the periodic solutions, and the analytical expressions for these solutions are given. Numerical simulation study demonstrates various types of bifurcations and the complex solution behaviors, such as cyclic fold bifurcation, period-doubling bifurcation, period-doubling cascade and chaotic orbits. All these results complement previous theoretical studies on the model, and contribute to a better understanding of the qualitative dynamics of the cancer model.