Hopf bifurcation analysis in the frequency domain for a 5D model of melanoma

This work studies the influence of the cytotoxic T lymphocyte (CTL) death rate on the bifurcation of a 5D melanoma model. The existence of Hopf bifurcation is analyzed using bifurcation theory and higher-order harmonic balance method in the frequency domain. In particular, the fourth-order harmonic balance approximations to the frequency and the amplitude of the periodic solution, and the analytical expressions for the solution are given. All the results verify that the CTL death rate is an important factor leading to the periodic oscillation of melanoma cell number.