Discrete and Continuous Dynamical Systems-Series B
We study finite-time perturbations of dynamical systems. We prove that finite-time perturbed dynamical systems are asymptotically equivalent to unperturbed dynamical systems. And so the asymptotical behavior of finite-time perturbed systems can be studied by unperturbed systems. As an example, we study a system perturbed by drug treatments.
Tian, J. P. (2009). Finite-time perturbations of dynamical systems and applications to tumor therapy. Appear to Discrete and Continuous Dynamical Systems-B, 12.