skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Stochastic resonance in a generalized Von Foerster population growth model

Abstract

The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.

Authors:
;  [1]
  1. Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn (Estonia)
Publication Date:
OSTI Identifier:
22390604
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1629; Journal Issue: 1; Conference: AMiTaNS 14: 6. International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena (Bulgaria), 26 Jun - 1 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; CAPACITY; CORRELATIONS; FLUCTUATIONS; HUMAN POPULATIONS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; NOISE; NONLINEAR PROBLEMS; RESONANCE; STOCHASTIC PROCESSES

Citation Formats

Lumi, N., and Mankin, R.. Stochastic resonance in a generalized Von Foerster population growth model. United States: N. p., 2014. Web. doi:10.1063/1.4902281.
Lumi, N., & Mankin, R.. Stochastic resonance in a generalized Von Foerster population growth model. United States. doi:10.1063/1.4902281.
Lumi, N., and Mankin, R.. Wed . "Stochastic resonance in a generalized Von Foerster population growth model". United States. doi:10.1063/1.4902281.
@article{osti_22390604,
title = {Stochastic resonance in a generalized Von Foerster population growth model},
author = {Lumi, N. and Mankin, R.},
abstractNote = {The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.},
doi = {10.1063/1.4902281},
journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1629,
place = {United States},
year = {2014},
month = {11}
}