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Bifurcations of a Filippov ecological system with an A-type discontinuity boundary.
- Source :
-
Chaos, Solitons & Fractals . May2024, Vol. 182, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
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. • A planar Filippov system with A-type nonlinear discontinuity boundaries is studied. • Rich bifurcations occur, including a new one involving three nested limit cycles. • The detection of three limit cycles may be helpful for Hilbert's 16th problem. • The appearance of long transient phenomenon represents an alert for practitioners. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09600779
- Volume :
- 182
- Database :
- Academic Search Index
- Journal :
- Chaos, Solitons & Fractals
- Publication Type :
- Periodical
- Accession number :
- 177035300
- Full Text :
- https://doi.org/10.1016/j.chaos.2024.114834