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.
Citation: Leonid Shaikhet. Stability of a positive equilibrium state for a stochastically perturbed mathematical model ofglassy-winged sharpshooter population[J]. Mathematical Biosciences and Engineering, 2014, 11(5): 1167-1174. doi: 10.3934/mbe.2014.11.1167
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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.
Dear Editorial Board Members,
It is my pleasure to share with you the year-end report for AIMS Environmental Science. The journal continues to improve its quality as indicated by steady increases in the number of manuscripts received and the number of articles published over the past three years (Figure 1). We have received 69 submissions with 28 published online. The most downloaded and cited papers are listed in Tables 1 and 2. The top read article received more than 11390 downloads.
I would like to thank all the board members for serving on the Editorial Board and their dedication and contribution to the journal, especially to the editors for two special issues: Impacts of Microplastics in the Urban Environment Conference and Green built environment. The goal in 2020 is to solicit more manuscripts and increase paper citations. We will try our best to reduce the processing time and supply with a better experience for publication. To recognize the contribution of the Editorial Board members and authors during the years, we will continue to offer that (1) for authors invited, the article processing charge (APC) is automatically waived; (2) each editorial board member is entitled for some waivers. I am looking forward to continuing working with you to make the AIMS Environmental Science a sustainable and impactful journal. Please don’t hesitate to send me e-mails if you have new ideas and suggestions to help us to achieve this goal.

Yifeng Wang, Ph.D.
Editor in Chief, AIMS Environmental Science
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