<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

Online veröffentlicht: 01. Nov. 2019

Seitenbereich: 455 - 461

Eingereicht: 19. Feb. 2019

Akzeptiert: 02. Apr. 2019

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

Schlüsselwörter
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

Online veröffentlicht: 01. Nov. 2019

Seitenbereich: 455 - 461

Eingereicht: 19. Feb. 2019

Akzeptiert: 02. Apr. 2019

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

Schlüsselwörterdiffusion 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.

Schlüsselwörter
diffusion approximation, stochastic population dynamics