Periodic solution and its stability of a delayed Beddington-DeAngelis type predator-prey system with discontinuous control strategy

Li, W; Huang, L; Ji, J

Periodic solution and its stability of a delayed Beddington-DeAngelis type predator-prey system with discontinuous control strategy

Li, W Huang, L Ji, J

Permalink

Publisher:: WILEY
Publication Type:: Journal Article
Citation:: Mathematical Methods in the Applied Sciences, 2019, 42, (13), pp. 4498-4515
Issue Date:: 2019-09-15

Closed Access

	Filename	Description	Size
	mma.5673.pdf	Published version	660.37 kB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Li, W
dc.contributor.author	Huang, L
dc.contributor.author	Ji, J https://orcid.org/0000-0003-3280-5463
dc.date.accessioned	2020-05-08T05:24:47Z
dc.date.available	2020-05-08T05:24:47Z
dc.date.issued	2019-09-15
dc.identifier.citation	Mathematical Methods in the Applied Sciences, 2019, 42, (13), pp. 4498-4515
dc.identifier.issn	0170-4214
dc.identifier.issn	1099-1476
dc.identifier.uri	http://hdl.handle.net/10453/140588
dc.description.abstract	© 2019 John Wiley & Sons, Ltd. This paper investigates the periodic solution of a delayed Beddington-DeAngelis (BD) type predator-prey model with discontinuous control strategy. Firstly, the regularity and visibility analysis of the delayed predator-prey model is carried out by using the principle of differential inclusion. Secondly, the positiveness and boundeness of the solution is discussed by employing the comparison theorem. Based on the boundary conditions of the model and the Mawhin-like coincidence theorem, it is shown that the solution of the delayed BD system is asymptotically stable in finite time. Furthermore, it is found that there exists at least one periodic solution of the nonautonomous delayed predator-prey model by using the principle of topological degree and set value mapping. Specially, when the nonautonomous delayed BD system degenerates into an autonomous system, some criteria are obtained to guarantee the convergence behavior of the harvesting solutions for the corresponding autonomous delayed BD system. Finally, numerical examples are given to demonstrate the applicability and effectiveness of main results. It is worthy to point out that the discontinuous control strategy is superior to the continuous harvesting policies adopted in existing literature.
dc.language	English
dc.publisher	WILEY
dc.relation.ispartof	Mathematical Methods in the Applied Sciences
dc.relation.isbasedon	10.1002/mma.5673
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0102 Applied Mathematics
dc.subject.classification	Applied Mathematics
dc.title	Periodic solution and its stability of a delayed Beddington-DeAngelis type predator-prey system with discontinuous control strategy
dc.type	Journal Article
utslib.citation.volume	42
utslib.for	0102 Applied Mathematics
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
pubs.consider-herdc	false
dc.date.updated	2020-05-08T05:24:45Z
pubs.issue	13
pubs.publication-status	Published
pubs.volume	42
utslib.start-page	4498
utslib.citation.issue	13

Abstract:

© 2019 John Wiley & Sons, Ltd. This paper investigates the periodic solution of a delayed Beddington-DeAngelis (BD) type predator-prey model with discontinuous control strategy. Firstly, the regularity and visibility analysis of the delayed predator-prey model is carried out by using the principle of differential inclusion. Secondly, the positiveness and boundeness of the solution is discussed by employing the comparison theorem. Based on the boundary conditions of the model and the Mawhin-like coincidence theorem, it is shown that the solution of the delayed BD system is asymptotically stable in finite time. Furthermore, it is found that there exists at least one periodic solution of the nonautonomous delayed predator-prey model by using the principle of topological degree and set value mapping. Specially, when the nonautonomous delayed BD system degenerates into an autonomous system, some criteria are obtained to guarantee the convergence behavior of the harvesting solutions for the corresponding autonomous delayed BD system. Finally, numerical examples are given to demonstrate the applicability and effectiveness of main results. It is worthy to point out that the discontinuous control strategy is superior to the continuous harvesting policies adopted in existing literature.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/140588