Mathematical Biosciences and Engineering, 2014, 11(5): 1167-1174. doi: 10.3934/mbe.2014.11.1167.

Primary: 92D25, 92D40; Secondary: 34K20.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population

1. Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015

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.
  Article Metrics

Keywords stability in probability.; asymptotic mean square stability; stochastic perturbations; glassy-winged sharpshooter population; equilibrium point; Mathematical model

Citation: Leonid Shaikhet. Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population. Mathematical Biosciences and Engineering, 2014, 11(5): 1167-1174. doi: 10.3934/mbe.2014.11.1167


  • 1. Nonlinearity, 18 (2005), 913-936.
  • 2. Mathematics and Computers in Simulation (Special Issue "Delay Systems"), 45 (1998), 269-277.
  • 3. Discrete Dynamics in Nature and Society, 2007 (2007), 25 pp.
  • 4. Mathematical Biosciences, 175 (2002), 117-131.
  • 5. Springer-Verlag, Berlin, 1972.
  • 6. Applied Mathematical Modelling, 36 (2012), 5214-5228.
  • 7. Stochastic Analysis and Applications, 27 (2009), 409-429.
  • 8. Mathematical Biosciences, 196 (2005), 65-81.
  • 9. Springer, London, Dordrecht, Heidelberg, New York, 2011.
  • 10. Springer, Dordrecht, Heidelberg, New York, London, 2013.
  • 11. Mathematical Biosciences and Engineering, 11 (2014), 667-677.


This article has been cited by

  • 1. Fancheng Yin, Xiaoyan Yu, The Stationary Distribution and Extinction of Generalized Multispecies Stochastic Lotka-Volterra Predator-Prey System, Mathematical Problems in Engineering, 2015, 2015, 1, 10.1155/2015/479326
  • 2. Wei Sun, Ling Xue, Xiangyun Yan, Stability of a dengue epidemic model with independent stochastic perturbations, Journal of Mathematical Analysis and Applications, 2018, 10.1016/j.jmaa.2018.08.033

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Leonid Shaikhet, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved