Predicting fluctuations-caused regime shifts in a time delayed dynamics of an invading species

In this paper, we investigate early warning signals (EWS) of regime shifts in a density-dependent invading population model with time delay, in which the population density is assumed to be disturbed by intrinsic and extrinsic fluctuations. It is shown that the time delay and noises can cause the regime shifts between low and high population density states. The regime shift time (RST) as a function of noise intensity exhibits a maximum, which identifies the signature of the noise-enhanced stability of the low density state, while the time delay weakens the stability of the low density state. Applying the Kramers time technique, we also discuss the intersection point of the RST between low and high population density states, i.e., a critical point in the RST is found. Therefore, the critical point may give an EWS of regime shifts from one alternative state to another one for the changes in the noise parameters and time delay.