Random effects in population models with hereditary effects |
| |
| Authors: | Juan Lin Peter B Kahn |
| |
| Institution: | (1) Department of Surgery, State University of New York at Stony Brook, 11794 Stony Brook, N.Y., USA;(2) Department of Nuclear Physics, Weizmann Institute of Science, Rehovot, Israel;(3) Department of Physics, State University of New York at Stony Brook, 11794 Stony Brook, N.Y., USA |
| |
| Abstract: | This paper discusses the influence of environmental noise on the dynamics of single species population models with hereditary effects. A detailed analysis is carried out for the logistic equation with discrete delay in the resource limitation term (Hutchinson's equation). When the system undergoes Hopf bifurcation, we find the stationary probability density distribution for the amplitude of the periodic solution by means of an averaged Fokker-Planck equation. Finally, we estimate the persistence time of the species when the population density has a lower bound beyond which it goes extinct. |
| |
| Keywords: | Differential-difference equations Hopf bifurcation Fokker-Planck equation Averaging method |
| 本文献已被 SpringerLink 等数据库收录！ |
|
