Bifurcations of a Filippov ecological system with an A-type discontinuity boundary

Zhu, Y; Zhang, Z; Ji, J

Bifurcations of a Filippov ecological system with an A-type discontinuity boundary

Zhu, Y Zhang, Z Ji, J

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Publisher:: PERGAMON-ELSEVIER SCIENCE LTD
Publication Type:: Journal Article
Citation:: Chaos, Solitons and Fractals, 2024, 182
Issue Date:: 2024-05-01

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Field	Value	Language
dc.contributor.author	Zhu, Y
dc.contributor.author	Zhang, Z
dc.contributor.author	Ji, J https://orcid.org/0000-0003-3280-5463
dc.date.accessioned	2025-02-04T00:49:46Z
dc.date.available	2025-02-04T00:49:46Z
dc.date.issued	2024-05-01
dc.identifier.citation	Chaos, Solitons and Fractals, 2024, 182
dc.identifier.issn	0960-0779
dc.identifier.issn	1873-2887
dc.identifier.uri	http://hdl.handle.net/10453/184908
dc.description.abstract	Based on the integrated pest management strategy, this paper proposes a Filippov pest–natural enemy system with a novel threshold control strategy. We not only incorporate the changing rate into the control index of the pest population but also consider a threshold value for the natural enemy. This novel threshold policy presents the discontinuity boundary as a complicated ‘A’ type, which induces abundant and complex sliding dynamics. Through theoretical analysis, both curve boundaries could have at most six sliding segments and two pseudo-equilibria, while the other straight line boundary could have a unique stable sliding segment with two pseudo-equilibria. Numerically, the sliding mode bifurcation confirms that the system can have six sliding segments and two pseudo-equilibria simultaneously. Particularly, we discover a new global bifurcation phenomenon that may be termed as a triple limit cycle bifurcation, which reveals the coexistence of three nested limit cycles, various bistable states of two nested or independent attractors, as well as the appearance of a meaningful long transient. Our results not only demonstrate the important effect of nonlinear boundaries but also provide a new perspective on practical pest control problems.
dc.language	English
dc.publisher	PERGAMON-ELSEVIER SCIENCE LTD
dc.relation.ispartof	Chaos, Solitons and Fractals
dc.relation.isbasedon	10.1016/j.chaos.2024.114834
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	01 Mathematical Sciences, 08 Information and Computing Sciences, 09 Engineering
dc.subject.classification	Mathematical Physics
dc.subject.classification	40 Engineering
dc.subject.classification	46 Information and computing sciences
dc.subject.classification	49 Mathematical sciences
dc.title	Bifurcations of a Filippov ecological system with an A-type discontinuity boundary
dc.type	Journal Article
utslib.citation.volume	182
utslib.for	01 Mathematical Sciences
utslib.for	08 Information and Computing Sciences
utslib.for	09 Engineering
pubs.organisational-group	University of Technology Sydney
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/UTS Groups
pubs.organisational-group	University of Technology Sydney/UTS Groups/Transport Research Centre (TRC)
pubs.organisational-group	University of Technology Sydney/UTS Groups/Centre for Audio, Acoustics and Vibration (CAAV)
pubs.organisational-group	University of Technology Sydney/UTS Groups/Transport Research Centre (TRC)/Transport Research Centre (TRC) Associate Members
utslib.copyright.status	closed_access	*
dc.date.updated	2025-02-04T00:49:45Z
pubs.publication-status	Published
pubs.volume	182

Abstract:

Based on the integrated pest management strategy, this paper proposes a Filippov pest–natural enemy system with a novel threshold control strategy. We not only incorporate the changing rate into the control index of the pest population but also consider a threshold value for the natural enemy. This novel threshold policy presents the discontinuity boundary as a complicated ‘A’ type, which induces abundant and complex sliding dynamics. Through theoretical analysis, both curve boundaries could have at most six sliding segments and two pseudo-equilibria, while the other straight line boundary could have a unique stable sliding segment with two pseudo-equilibria. Numerically, the sliding mode bifurcation confirms that the system can have six sliding segments and two pseudo-equilibria simultaneously. Particularly, we discover a new global bifurcation phenomenon that may be termed as a triple limit cycle bifurcation, which reveals the coexistence of three nested limit cycles, various bistable states of two nested or independent attractors, as well as the appearance of a meaningful long transient. Our results not only demonstrate the important effect of nonlinear boundaries but also provide a new perspective on practical pest control problems.

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

http://hdl.handle.net/10453/184908