The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator
Joint Authors
Carkovs, Jevgeņijs
Goldšteine, Jolanta
Šadurskis, Kārlis
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-20
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We present the analysis of a mathematical model of the dynamics of interacting predator and prey populations with the Holling type random trophic function under the assumption of random time interval passage between predator attacks on prey.
We propose a stochastic approximation algorithm for quantitative analysis of the above model based on the probabilistic limit theorem.
If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion.
Assuming that the averaged dynamical system is the classic Holling type II population model with asymptotically stable limit cycle, we prove that the dynamics of stochastic model may be approximated with a two-dimensional Gaussian Markov process with unboundedly increasing variances.
American Psychological Association (APA)
Carkovs, Jevgeņijs& Goldšteine, Jolanta& Šadurskis, Kārlis. 2018. The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1176031
Modern Language Association (MLA)
Carkovs, Jevgeņijs…[et al.]. The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator. Journal of Applied Mathematics No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1176031
American Medical Association (AMA)
Carkovs, Jevgeņijs& Goldšteine, Jolanta& Šadurskis, Kārlis. The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1176031
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176031