A Quantification of Long Transient Dynamics

The stability of equilibria and asymptotic behaviors trajectories are often the primary focuses mathematical modeling. However, many interesting phenomena that we would like to model, such as “honeymoon period” a disease after onset mass vaccination programs, transient dynamics. Honeymoon periods can last for decades be important public health considerations. In fields science, especially in ecology, there is growing interest systematic study this work, attempt provide technical definition “long dynamics” honeymoon period explain how these arise systems ordinary differential equations. We define center, point state space causes long behaviors, derive some its properties. end, reachable centers, which centers reached from initializations do not need near center.