A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment

Author:

Sabbar Yassine1,Palencia José Luis Diaz23,Tilioua Mouhcine1,Otero Abraham2,Zeb Anwar4,Djilali Salih5

Affiliation:

1. MAIS Laboratory, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P. O. Box 509, Errachidia 52000, Morocco

2. Department of Information Technology, Escuela Politecnica Superior, Universidad San Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, Spain

3. Department of Mathematics and Education, Universidad a Distancia de Madrid, Spain

4. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Khyber Pakhtunkhwa, Pakistan

5. Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria

Abstract

<abstract><p>A chemostat is a laboratory device (of the bioreactor type) in which organisms (bacteria, phytoplankton) develop in a controlled manner. This paper studies the asymptotic properties of a chemostat model with generalized interference function and Poisson noise. Due to the complexity of abrupt and erratic fluctuations, we consider the effect of the second order Itô-Lévy processes. The dynamics of our perturbed system are determined by the value of the threshold parameter $ \mathfrak{C}^{\star}_0 $. If $ \mathfrak {C}^{\star}_0 $ is strictly positive, the stationarity and ergodicity properties of our model are verified (<italic>practical scenario</italic>). If $ \mathfrak {C}^{\star}_0 $ is strictly negative, the considered and modeled microorganism will disappear in an exponential manner. This research provides a comprehensive overview of the chemostat interaction under general assumptions that can be applied to various models in biology and ecology. In order to verify the reliability of our results, we probe the case of industrial waste-water treatment. It is concluded that higher order jumps possess a negative influence on the long-term behavior of microorganisms in the sense that they lead to complete extinction.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3