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

Yuxun Zhu, Zhengdi Zhang and Jinchen Ji

Chaos, Solitons & Fractals, 2024, vol. 182, issue C

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.

Keywords: Filippov system; Integrated pest management; Triple limit cycle bifurcation; Long transient (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003862

DOI: 10.1016/j.chaos.2024.114834

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