title: Stability of a positive equilibrium state for a stochastically perturbed mathematical model of glassy-winged sharpshooter population.
abstract: 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.
authors.affiliation: Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015, Ukraine. leonid.shaikhet@usa.net.
authors.forename: Leonid
authors.initials: L
authors.lastname: Shaikhet
mesh_terms: D000818:Animals; D006430:Hemiptera / Q000254:growth & development*; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D011156:Population Density; D013269:Stochastic Processes