  This paper investigates biological models that represent the transition
equation from a system in the past to a system in the future. It is shown that
finite-time Lyapunov exponents calculated along a locally pullback attractive
solution are efficient indicators (early-warning signals) of the presence of a
tipping point. Precise time-dependent transitions with concave or d-concave
variation in the state variable giving rise to scenarios of rate-induced
tracking are shown. They are classified depending on the internal dynamics of
the set of bounded solutions. Based on this classification, some representative
features of these models are investigated by means of a careful numerical
analysis.
