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ASYMPTOTIC BEHAVIOUR OF A CLASS OF RESOURCE COMPETITION BIOLOGY SPECIES SYSTEM BY THE FRACTIONAL BROWNIAN MOTION

Published online by Cambridge University Press:  15 May 2017

Q. ZHANG ,
M. YE ,
H. LEI  and
Q. JIN
Q. ZHANG
Affiliation:
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, PR China email zhangqimin64@sina.com, zhangqimin@nxu.edu.cn
M. YE*
Affiliation:
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA email mye@fsu.edu, hl15e@my.fsu.edu
H. LEI
Affiliation:
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA email mye@fsu.edu, hl15e@my.fsu.edu
Q. JIN
Affiliation:
Department of Geological Sciences, University of Oregon, Eugene, OR 97403-1272, USA email qjin@uoregon.edu
*
✉ mye@fsu.edu, hl15e@my.fsu.edu
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Abstract

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We analyse the asymptotic behaviour of a biological system described by a stochastic competition model with $n$ species and $k$ resources (chemostat model), in which the species mortality rates are influenced by the fractional Brownian motion of the extrinsic noise environment. By constructing a Lyapunov functional, the persistence and extinction criteria are derived in the mean square sense. Some examples are given to illustrate the effectiveness of the theoretical result.

Keywords

resource competitionbiology species systemfractional Brownian motionpersistenceextinction

MSC classification

Primary: 92D30: Epidemiology

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 491 - 499
Copyright
© 2017 Australian Mathematical Society 

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