Abstract. We discuss a sufficient condition which guarantees the existence and uniqueness of non-negative solutions to an initial value problem of non-autonomous ODE systems, which include a cardiac hypertrophy network model as one of the typical examples of ODE systems induced from biochemical reaction networks by applying the low of mass action, and show the non-negativity of the solutions to the model. Moreover, we define a dynamic equilibrium point of the cardiac hypertrophy network model, which is non-autonomous, and analyze its structure theoretically as well as investigating the convergence of global-in-time solutions to the dynamic equilibrium point using numerical simulations.