A NOTE ON A CLASS OF DISCRETE LARGE- AND SUB-CENTRE SYSTEMS

Yanglan Ou; Hongfeng Ren; Guang Zhang; Qiru Wang

doi:10.11948/20250352

2026 Volume 16 Issue 5

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Yanglan Ou, Hongfeng Ren, Guang Zhang, Qiru Wang. A NOTE ON A CLASS OF DISCRETE LARGE- AND SUB-CENTRE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2771-2778. doi: 10.11948/20250352

Citation:

Yanglan Ou, Hongfeng Ren, Guang Zhang, Qiru Wang. A NOTE ON A CLASS OF DISCRETE LARGE- AND SUB-CENTRE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2771-2778. doi: 10.11948/20250352

A NOTE ON A CLASS OF DISCRETE LARGE- AND SUB-CENTRE SYSTEMS

1.
School of Pharmacy, Guangzhou Xinhua University, 19 Huamei Road, Tianhe District, Guangzhou 510520, Guangdong, China
2.
Zhujiang College, South China Agricultural University, Guangzhou 510900, Guangdong, China
3.
School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai 519082, Guangdong, China

Author Bio: Email: qd gzhang@126.com(G. Zhang); Email: mcswqr@mail.sysu.edu.cn(Q. Wang)
Corresponding authors: Email: ownerounan@163.com(Y. Ou); Email: hf.ren@163.com(H. Ren)
Fund Project: The authors were supported by Doctoral guidance program of Guangzhou Xinhua University, the Characteristic Innovation Projects of Ordinary Universities in Guangdong [Nos. 2024KTSCX098, 2025KTSCX242], School level Scientific Research Project of the Zhujiang College of South China Agricultural University under Grant number [Nos. 2024ZJKYC004, 2024ZJKYC068]

Abstract

Abstract

For different mappings, there are various methods and techniques to obtain the normal forms and calculate the center manifolds of a system, with the computations being highly complicated. Unfortunately, all the results obtained are merely of a local nature. Recently, a discrete logistic-lottery system with large- and sub-centres was studied. The authors established a flip bifurcation theorem and provided some numerical simulations. Thus, they demonstrated that the lottery competition is indeed driven by the logistic growth of the dominant species. In this note, we have once again considered that system and theoretically proved that all its stable periodic solutions are induced by the main equation. In particular, the method is remarkably straightforward, and the logistic model can be generalized to other recursive equations, such as those describing the weak Allee effect, the strong Allee effect, the Ricker model, or the Caspari-Watson function.
- Large- and sub-centre /
- discrete system /
- periodic solution /
- chaos
MSC: 39A10, 39A28, 39A30

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