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http://hdl.handle.net/1942/44406
Title: | Cyclicity of slow–fast cycles with one self-intersection point and two nilpotent contact points | Authors: | YAO, Jinhui Huang, Jicai HUZAK, Renato Ruan, Shigui |
Issue Date: | 2024 | Source: | Nonlinearity, 37 (11) (Art N° 115007) | Abstract: | In this paper, we study the cyclicity of slow–fast cycles with one self-intersection point and two nilpotent contact points in planar slow–fast systems, where the nilpotent contact point is a jump point or a slow–fast Hopf point. These slow–fast cycles can be classified into three cases based on the two nilpotent contact points: (i) both are generic jump points, (ii) one is a generic jump point and the other is a slow–fast Hopf point, and (iii) both are slow–fast Hopf points. By using slow divergence integrals and entry–exit functions, we show that the cyclicity of slow–fast cycles with one self-intersection point and two generic jump points (or one generic jump point and one slow–fast Hopf point) is at most two, and the cyclicity of slow–fast cycles with one self-intersection point and two slow–fast Hopf points is at most three under some specific conditions. Finally, we apply the main results to two predator-prey models. | Keywords: | slow-fast cycles;self-intersection point;nilpotent contact point;cyclicity;entry-exit function;slow divergence integral;difference map AMS subject classifications 34027;34C26;34E15 | Document URI: | http://hdl.handle.net/1942/44406 | ISSN: | 0951-7715 | e-ISSN: | 1361-6544 | DOI: | 10.1088/1361-6544/ad7c11 | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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YHHR_20240812.pdf Until 2025-04-01 | Peer-reviewed author version | 2.95 MB | Adobe PDF | View/Open Request a copy |
Yao_2024_Nonlinearity_37_115007.pdf Restricted Access | Published version | 6.04 MB | Adobe PDF | View/Open Request a copy |
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