Cancer model and its possible control-A Z-type control approach.

This paper investigates the dynamics of a three-dimensional nonlinear cancer model involving interactions among cancer cells, normal cells, and immune cells. By performing a linear stability analysis of the equilibria and investigating the Hopf bifurcation in relation to the immune cell growth rate, we reveal the possibility of chaotic behavior when radiation is absent. However, with the appropriate implementation of radiotherapy, the cancer model demonstrates stable solutions, transitioning from chaotic oscillations through period-halving bifurcation.