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Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-11
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We investigate a stochastic Food-Chain System d x ( t ) = [ r 1 ( t ) - a 11 ( t ) x - ( a 12 ( t ) y / ( 1 + β 1 ( t ) x + γ 1 ( t ) y ) ) ] x d t + σ 1 ( t ) x d B 1 ( t ) , d y ( t ) = [ r 2 ( t ) - a 21 ( t ) y + ( a 22 ( t ) x / ( 1 + β 1 ( t ) x + γ 1 ( t ) y ) ) - ( a 23 ( t ) z / ( 1 + β 2 ( t ) y + γ 2 ( t ) z ) ) ] y d t + σ 2 ( t ) y d B 2 ( t ) , d z ( t ) = [ - r 3 ( t ) + ( a 3 1 ( t ) y / ( 1 + β 2 ( t ) y + γ 2 ( t ) z ) ) - a 32 ( t ) z ] z d t + σ 3 ( t ) z d B 3 ( t ) , where B i ( t ) , i = 1 , 2 , 3 , is a standard Brownian motion.
Firstly, the existence, the uniqueness, and the positivity of the solution are proved.
Secondly, the stochastically ultimate boundedness of the system is investigated.
Thirdly, the boundedness of moments and upper-growth rate of the solution are obtained.
Then the global attractivity of the system is discussed.
Finally, the main results are illustrated by several examples.
American Psychological Association (APA)
Ge, Yanming& Song, Zigen. 2014. Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-1013915
Modern Language Association (MLA)
Ge, Yanming& Song, Zigen. Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response. Abstract and Applied Analysis No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-1013915
American Medical Association (AMA)
Ge, Yanming& Song, Zigen. Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-1013915
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013915