Abstract
We carry out qualitative analysis of a fourth‐order tumor growth control model using ordinary differential equations. We show that the system has one positive equilibrium point, and its stability is independent of the feedback gain. Using a Lyapunov function method, we prove that there exist realistic parameter values for which the systems admit limit cycle oscillations due to a supercritical Hopf bifurcation. The time evolution of the state variables is also represented.
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