Open AccessAsymptotic behavior of a delayed stochastic logistic model with impulsive perturbations
Author(s) -
Sanling Yuan,
Xuehui Ji,
Huaiping Zhu
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017077
Subject(s) - uniqueness , mathematics , stationary distribution , impulse (physics) , white noise , perturbation (astronomy) , markov chain , population model , markov process , population , statistical physics , mathematical analysis , statistics , physics , demography , quantum mechanics , sociology
In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. By using the theory of integral Markov semigroups, we further derive sufficient conditions for the existence of the stationary distribution of the system. Finally, we perform the extinction analysis of the model. Numerical simulations illustrate the obtained theoretical results.