<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive stochastic Poisson-type differential equations with a small parameter and propose an approximative algorithm for quantitative analysis of population dynamics that consists of two steps. First, we derive an ordinary differential equation for mean value of each population growth and analyse the average asymptotic population behaviour. Then, applying diffusion approximation procedure, we derive a stochastic Ito differential equation for small random deviations on the average motion in a form of a linear non-homogeneous Ito stochastic differential equation and analyse the probabilistic characteristics of the Gaussian process given by this equation.</p></abstract>

The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive stochastic Poisson-type differential equations with a small parameter and propose an approximative algorithm for quantitative analysis of population dynamics that consists of two steps. First, we derive an ordinary differential equation for mean value of each population growth and analyse the average asymptotic population behaviour. Then, applying diffusion approximation procedure, we derive a stochastic Ito differential equation for small random deviations on the average motion in a form of a linear non-homogeneous Ito stochastic differential equation and analyse the probabilistic characteristics of the Gaussian process given by this equation.

Stochastic Modelling for Dynamics of Interacting Populations

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Stochastic Modelling for Dynamics of Interacting Populations"}

The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive...

Stochastic Modelling for Dynamics of Interacting Populations

Published Online: Nov 01, 2019

Page range: 455 - 461

Received: Feb 19, 2019

Accepted: Apr 02, 2019

DOI: https://doi.org/10.2478/prolas-2019-0070

Keywords
diffusion approximation, stochastic population dynamics

© 2019 Jevgeņijs Carkovs et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Stochastic Modelling for Dynamics of Interacting Populations

Published Online: Nov 01, 2019

Page range: 455 - 461

Received: Feb 19, 2019

Accepted: Apr 02, 2019

DOI: https://doi.org/10.2478/prolas-2019-0070

Keywordsdiffusion approximation, stochastic population dynamics

© 2019 Jevgeņijs Carkovs et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
diffusion approximation, stochastic population dynamics