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Stability switching and hopf bifurcation in a two-delay predation system with diffusion and network coupling |
| Wenjie Yang(杨文杰)1,2,3, Jingxin Hu(胡静欣)1,4, Qianqian Zheng(郑前前)1, Jianwei Shen(申建伟)4,†, and Yiping Lin(林怡平)5 |
1 School of Science, Xuchang University, Xuchang 461000, China;
2 Complex Systems Research Center, Shanxi University, Taiyuan 030006, China;
3 Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis for Disease Control and Prevention, Taiyuan 030006, China;
4 School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China;
5 Department of Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, China |
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Abstract This paper studies stability switching and Hopf bifurcation in a two-delay predation system with diffusion and network coupling. By using the Kronecker-product formulation and Laplacian-mode decomposition, the high-dimensional characteristic equation of the coupled system is reduced to a family of mode-dependent characteristic equations. Based on this reduction, explicit stability-switching curves are derived in the $(\tau_1,\tau_2)$-plane, and the corresponding stability region of the positive equilibrium is determined. Furthermore, by applying the Hassard method and center-manifold reduction, the direction of the Hopf bifurcation, the stability of the bifurcating periodic solutions, and the variation of their periods are obtained. Numerical examples are presented to verify the theoretical results and illustrate the temporal and spatiotemporal dynamics generated by the two delays under network coupling. These results provide an effective analytical framework for studying delay-induced stability switching and oscillatory behavior in networked predator-prey systems.
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Received: 18 January 2026
Revised: 02 April 2026
Accepted manuscript online: 08 April 2026
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PACS:
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02.30.-f
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(Function theory, analysis)
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02.30.Ks
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(Delay and functional equations)
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02.30.Oz
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(Bifurcation theory)
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02.30.Sa
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(Functional analysis)
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| Fund: This work is supported by the Key Scientific Research Project of Colleges and Universities in Henan Province(Grant No. 24B110017) and the Natural Science Foundation of Henan Province(Grant No. 242300420661). |
Corresponding Authors:
Jianwei Shen
E-mail: xcjwshen@gmail.com
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Cite this article:
Wenjie Yang(杨文杰), Jingxin Hu(胡静欣), Qianqian Zheng(郑前前), Jianwei Shen(申建伟), and Yiping Lin(林怡平) Stability switching and hopf bifurcation in a two-delay predation system with diffusion and network coupling 2026 Chin. Phys. B 35 080204
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