DYNAMICAL BEHAVIORS OF A DISCRETE TWO-DIMENSIONAL COMPETITIVE SYSTEM EXACTLY DRIVEN BY THE LARGE CENTRE

Binbin Du; Changjian Wu; Guang Zhang; Xiao-Liang Zhou

doi:10.11948/20230437

2024 Volume 14 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(5): 2822-2844

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Binbin Du, Changjian Wu, Guang Zhang, Xiao-Liang Zhou. DYNAMICAL BEHAVIORS OF A DISCRETE TWO-DIMENSIONAL COMPETITIVE SYSTEM EXACTLY DRIVEN BY THE LARGE CENTRE[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2822-2844. doi: 10.11948/20230437

Citation:

Binbin Du, Changjian Wu, Guang Zhang, Xiao-Liang Zhou. DYNAMICAL BEHAVIORS OF A DISCRETE TWO-DIMENSIONAL COMPETITIVE SYSTEM EXACTLY DRIVEN BY THE LARGE CENTRE[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2822-2844. doi: 10.11948/20230437

DYNAMICAL BEHAVIORS OF A DISCRETE TWO-DIMENSIONAL COMPETITIVE SYSTEM EXACTLY DRIVEN BY THE LARGE CENTRE

1.
Aviation Foundation College, Naval Aviation University, 264001 Yantai, Shandong, China
2.
Institute of Nonlinear Complexity, Zhujiang College of South China Agricultural University, 510900 Guangzhou, Guangdong, China
3.
School of Mathematics and Statistics, Lingnan Normal University, 524048 Zhanjiang, Guangdong, China

Author Bio: Email: dubinbin2006@sohu.com(B. B. Du); Email: zxlmath@163.com(X. L. Zhou)
Corresponding authors: Email: wchjianyf@163.com(C. J. Wu); Email: qd_gzhang@126.com(G. Zhang)
Fund Project: The authors were supported by the Characteristic Innovation Projects of Ordinary Universities in Guangdong (Natural Science) (No. 2023KTSCX184) and Natural Science Foundation of Guangdong Province (No. 2022A1515010964)

Abstract

Abstract

In this paper, a new discrete large-sub-center system is obtained by using the Euler and nonstandard discretization methods for the corresponding continuous system. It is surprised that all dynamic behaviors of the discrete system are exactly driven by the large-center equation, for example, the stabilities, the bifurcations, the period-doubling orbits, and the chaotic dynamics, etc. Additionally, the global asymptotical stability, the existence of exact 2-periodic solutions, the flip bifurcation theorem, and the invariant set of the sub-center equation is also given. These results reveal far richer dynamics of the discrete model compared with the continuous model. Through numerical simulation, we can observe some complex dynamic behaviors, such as period-doubling cascade, periodic windows, chaotic dynamics, etc. Especially, our theoretical results are also showed by those numerical simulations.
- Large-sub-center /
- discrete system /
- flip bifurcation /
- center manifold method /
- chaos
MSC: 39A28, 39A30

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References

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