A kinetic model with time‐dependent proliferative/destructive rates

Abstract

This paper presents a new kinetic model with time‐dependent proliferative/destructive parameters, where the activity variable of the system attains its values in a discrete real subset. Therefore, a system of nonautonomous nonlinear ordinary differential equations is gained, with the related Cauchy problem. A first result of local existence and uniqueness of positive and bounded solution is proved. Then, the possibility of extend this result globally in time is discussed, with respect to the shape of nonconservative time‐dependent parameters. Numerical simulations are performed for some scenarios, corresponding to different shapes of time‐dependent parameters themselves. Furthermore, the pattern and long‐time behavior of solutions are numerically analyzed. Finally, these results show that equilibria and oscillations may occur.