Impact of Colored Noise on Population Model with Allee Effect**Supported by the National Natural Science Foundation of China Grant No.11571009, Shanxi Scholarship Council of China under Grant No. 2015-032, Technological Innovation Programs of Higher Education Institutions in Shanxi Grant No. 2015121 and Applied Basic Research Programs of Shanxi Province Grant No. 2016021013

Abstract

We study a population model with strong and weak Allee effect driven by internal noise and external noise. Firstly, a single-species population model with Allee effect under environmental colored noise is established, then stable and unstable states are analyzed and interpreted in biology. After that, stationary probability distribution (SPD) of population is derived based on Fokker-Planck equation. Next, mean first-passage time (MFPT) is defined in order to quantify the transition between extinction state and survival state with Allee effect. It is found that population will not extinct when weak Allee effect exists. It is not beneficial to survival of the population with the increase of Allee threshold no matter whether strong Allee effect or weak Allee effect. When strong Allee effect occurs, the correlation time of multiplicative noise plays a positive role in survival of population, while the correlation time of additive noise has a negative effect. Crucially, the phenomenon of resonant activation is firstly discovered in population dynamics with Allee effect. The conclusions we obtain can be applied to the further research of population dynamics in ecology.