Stochastic periodic solution for a perturbed non-autonomous predator–prey model with generalized nonlinear harvesting and impulses

Yan Zhang, Shihua Chen, Shujing Gao and Xiang Wei

Physica A: Statistical Mechanics and its Applications, 2017, vol. 486, issue C, 347-366

Abstract: In this paper, stochastic non-autonomous predator–prey models with and without impulses are investigated. The effects of generalized nonlinear harvesting for prey and predator populations are considered. For the stochastic system without impulses, the existence and uniqueness of the positive solution is proven and sufficient conditions that guarantee the extinction and persistence of the population in the mean are achieved. We show the existence of a nontrivial positive periodic solution by constructing appropriate Lyapunov functions and using Khasminskii’s theory. Moreover, the global attractiveness and stochastic persistence in probability of the stochastic model are discussed. Results show that the stronger noises and nonlinear harvesting component can significantly influence the dynamics of the system and lead to the extinction of the predator population. Additionally, for the stochastic predator–prey system with impulsive effect, we prove that there exists a positive periodic solution. Numerical simulations are conducted to show the effectiveness and feasibility of the obtained results.

Keywords: Impulses; Nonlinear harvesting; Periodic solution; Stochastic perturbations (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437117305769
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:486:y:2017:i:c:p:347-366

DOI: 10.1016/j.physa.2017.05.058

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().