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Global exponential stability of periodic solutions to a delay Lasota-Wazewska model with discontinuous harvesting


Authors: Lian Duan, Lihong Huang and Yuming Chen
Journal: Proc. Amer. Math. Soc. 144 (2016), 561-573
MSC (2010): Primary 34A36; Secondary 34K09, 92D25
DOI: https://doi.org/10.1090/proc12714
Published electronically: May 28, 2015
MathSciNet review: 3430834
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Abstract: In this paper, we study a delay Lasota-Wazewska model with discontinuous harvesting, which is described by a periodic nonsmooth dynamical system. Based on a newly developed method, nonsmooth analysis, and the generalized Lyapunov method, easily verifiable delay-independent criteria are established to ensure the existence and global exponential stability of positive periodic solutions, which not only cover but also complement some existing ones. These theoretical results are also supported with numerical simulations.


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Additional Information

Lian Duan
Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People’s Republic of China
Email: lianduan0906@163.com

Lihong Huang
Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People’s Republic of China
Address at time of publication: Department of Information Technology, Hunan Women’s University, Changsha, Hunan 410004, People’s Republic of China
Email: lhhuang@hnu.edu.cn

Yuming Chen
Affiliation: Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5
Email: ychen@wlu.ca

DOI: https://doi.org/10.1090/proc12714
Keywords: Lasota-Wazewska model, positive periodic solution, global exponential stability, discontinuous harvesting, Lyapunov function.
Received by editor(s): September 6, 2014
Received by editor(s) in revised form: December 24, 2014
Published electronically: May 28, 2015
Additional Notes: This research was partially supported by the National Natural Science Foundation of China (11371127), Hunan Provincial Innovation Foundation for Postgraduate (CX2014B160), and the Natural Sciences and Engineering Research Council (NSERC) of Canada.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society