DYNAMICAL BEHAVIORS FOR A DISCRETE TWO-NEURON SYSTEM

Yanglan Ou; Haoyu Wang; Mingyao Wen; Guang Zhang; Qiru Wang

doi:10.11948/20250305

2026 Volume 16 Issue 4

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Yanglan Ou, Haoyu Wang, Mingyao Wen, Guang Zhang, Qiru Wang. DYNAMICAL BEHAVIORS FOR A DISCRETE TWO-NEURON SYSTEM[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1843-1859. doi: 10.11948/20250305

Citation:

Yanglan Ou, Haoyu Wang, Mingyao Wen, Guang Zhang, Qiru Wang. DYNAMICAL BEHAVIORS FOR A DISCRETE TWO-NEURON SYSTEM[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1843-1859. doi: 10.11948/20250305

DYNAMICAL BEHAVIORS FOR A DISCRETE TWO-NEURON SYSTEM

1.
School of Pharmacy, Guangzhou Xinhua University, 19 Huamei Road Tianhe District, 510520 Guangzhou, Guangdong, China
2.
Zhujiang College of South China Agricultural University, 510900 Guangzhou, Guangdong, China
3.
Guangdong Engineering Technology Research Center for Artificial Intelligence Empowered Media Technologies and Applications, 510900 Guangzhou, Guangdong, China
4.
School of Mathematics (Zhuhai), Sun Yat-Sen University, 519082 Zhuhai, Guangdong, China

Author Bio: Email: ownerounan@163.com(Y. Ou); Email: why_8199@qq.com(H. Wang); Email: mcswqr@mail.sysu.edu.cn(Q. Wang)
Corresponding authors: Email: gzmywen@126.com(M. Wen); Email: qd_gzhang@126.com(G. Zhang)
Fund Project: This work was supported by the Characteristic Innovation Projects of Ordinary Universities in Guangdong (Nos. 2023KTSCX184, 2024ZJKYC068, 2025KTSCX242) and National College Student Innovation and Entrepreneurship Training Program in China (No. 202512623007)

Abstract

Abstract

In this paper, a discrete two-neuron system is investigated, wherein the comparison principle, invariant sets, existence, non-existence, and stability of steady-state solutions are established. These results are new, sharp, and valid for high-dimensional systems. Numerical simulations not only confirmed the obtained theoretical results but also inspired some new reflections. Furthermore, a new local stability theorem and its corollary are derived by applying the Courant-Weyl inequalities. In particular, the obtained theoretical results and numerical simulations will be beneficial for more general bistable discrete systems.
- Discrete Nagumo equation /
- comparison principle /
- invariant interval /
- stability
MSC: 15A99, 39A10

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References

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