Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population
The known nonlinear mathematical model of the Glassy-winged Sharpshooter is considered. It is assumed that this model is influenced by stochastic perturbations of the white noise type and these perturbations are directly proportional to the deviation of the system state from the positive equilibrium...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1167 |
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| author | Leonid Shaikhet |
| author_facet | Leonid Shaikhet |
| author_sort | Leonid Shaikhet |
| collection | DOAJ |
| description | The known nonlinear mathematical model of the Glassy-winged Sharpshooter is considered. It is assumed that this model is influenced by stochastic perturbations of the white noise type and these perturbations are directly proportional to the deviation of the system state from the positive equilibrium point. A necessary and sufficient condition for asymptotic mean square stability of the equilibrium point of the linear part of the considered stochastic differential equation is obtained. This condition is at the same time a sufficient one for stability in probability of the equilibrium point of the initial nonlinear equation. Numerical calculations and figures illustrate the obtained results. |
| format | Article |
| id | doaj-art-26133b4835d540d7ac5d91ef98d9283a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-26133b4835d540d7ac5d91ef98d9283a2025-01-24T02:28:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-05-011151167117410.3934/mbe.2014.11.1167Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter populationLeonid Shaikhet0Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015The known nonlinear mathematical model of the Glassy-winged Sharpshooter is considered. It is assumed that this model is influenced by stochastic perturbations of the white noise type and these perturbations are directly proportional to the deviation of the system state from the positive equilibrium point. A necessary and sufficient condition for asymptotic mean square stability of the equilibrium point of the linear part of the considered stochastic differential equation is obtained. This condition is at the same time a sufficient one for stability in probability of the equilibrium point of the initial nonlinear equation. Numerical calculations and figures illustrate the obtained results.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1167stability in probability.asymptotic mean square stabilitystochastic perturbationsglassy-winged sharpshooter populationequilibrium pointmathematical model |
| spellingShingle | Leonid Shaikhet Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population Mathematical Biosciences and Engineering stability in probability. asymptotic mean square stability stochastic perturbations glassy-winged sharpshooter population equilibrium point mathematical model |
| title | Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population |
| title_full | Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population |
| title_fullStr | Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population |
| title_full_unstemmed | Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population |
| title_short | Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population |
| title_sort | stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy winged sharpshooter population |
| topic | stability in probability. asymptotic mean square stability stochastic perturbations glassy-winged sharpshooter population equilibrium point mathematical model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1167 |
| work_keys_str_mv | AT leonidshaikhet stabilityofapositiveequilibriumstateforastochasticallyperturbedmathematicalmodelofglassywingedsharpshooterpopulation |