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Bifurcation and Stability Analysis for a Class of Discrete Singular Predator-Prey System
Research Article | Published: 07 March 2026
Journal of Nonlinear Dynamics and Applications Volume 2, Issue 1, 2026: 39-46
Volume 2, Issue 1, Journal of Nonlinear Dynamics and Applications
Volume 2, Issue 1, 2026
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Journal of Nonlinear Dynamics and Applications, Volume 2, Issue 1, 2026: 39-46

Free to Read | Research Article | 07 March 2026
Bifurcation and Stability Analysis for a Class of Discrete Singular Predator-Prey System
by
Jing Han Jing Han 1 *
Wei Liu Wei Liu 2
1 School of Information Engineering, Wuhan Business University, Wuhan 430000, China
2 School of Information Management and Mathematics, Jiangxi University of Finance and Economics, Nanchang 330032, China
* Corresponding Author: Jing Han, [email protected]
DOI: 10.62762/JNDA.2026.505976
ARK: ark:/57805/jnda.2026.505976
Received: 15 November 2025, Accepted: 03 March 2026, Published: 07 March 2026  
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Abstract
A kind of discrete-time singular predator-prey system with time-varying harvesting term is investigated. By using theory of singular systems, bifurcation and center manifold theory, the stability and Neimark-Sacker bifurcation of such system is studied, and some conditions are used to judge local stability of its fixed points and ensure existence of the Neimark-Sacker bifurcation for the proposed discrete-time singular system are derived. Finally, numerical simulations are given to show the obtained results. The results of the paper complements some previous works, and we believe that the method of this paper can be used to study bifurcation for other discrete-time complex singular systems.
Graphical Abstract
Bifurcation and Stability Analysis for a Class of Discrete Singular Predator-Prey System
Keywords
stability
neimark-Sacker bifurcation
predator-prey
discrete-time
singular system
Data Availability Statement
Data will be made available on request.
Funding
This work was supported by the National Science Foundation of China under Grant 62506273, and also supported by the Science and Technology Project of the Education Department of Jiangxi Province under Grant GJJ210512.
Conflicts of Interest
The authors declare no conflicts of interest.
AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
References
  1. Holling, C. S. (1965). The functional response of predators to prey density and its role in mimicry and population regulation. The Memoirs of the Entomological Society of Canada, 97(S45), 5-60.
    [CrossRef]   [Google Scholar]
  2. Din, Q. (2017). Complexity and chaos control in a discrete-time prey-predator model. Communications in nonlinear science and numerical simulation, 49, 113-134.
    [CrossRef]   [Google Scholar]
  3. He, Z., & Lai, X. (2011). Bifurcation and chaotic behavior of a discrete-time predator–prey system. Nonlinear Analysis: Real World Applications, 12(1), 403-417.
    [CrossRef]   [Google Scholar]
  4. Li, Y. Y., Zhang, F. X., & Zhuo, X. L. (2019). Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes. Mathematical biosciences and engineering: MBE, 17(3), 2003-2015.
    [CrossRef]   [Google Scholar]
  5. Mortuja, M. G., Chaube, M. K., & Kumar, S. (2023). Bifurcation analysis of a discrete type prey-predator model with Michaelis–Menten harvesting in predator. Zeitschrift für Naturforschung A, 78(6), 499-510.
    [CrossRef]   [Google Scholar]
  6. Al Khabyah, A., Ahmed, R., Akram, M. S., & Akhtar, S. (2023). Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect. AIMS Mathematics, 8(4), 8060.
    [CrossRef]   [Google Scholar]
  7. Huang, K., Jia, X., Zhang, Y., Li, Y., & Li, C. (2026). Bifurcation and chaos in a discrete-time predator-prey system with strong Allee effect. Communications in Nonlinear Science and Numerical Simulation, 109794.
    [CrossRef]   [Google Scholar]
  8. Hu, D., & Cao, H. (2017). Stability and bifurcation analysis in a predator–prey system with Michaelis–Menten type predator harvesting. Nonlinear Analysis: Real World Applications, 33, 58-82.
    [CrossRef]   [Google Scholar]
  9. Wang, Y., Zhou, X., & Jiang, W. (2023). Bifurcations in a diffusive predator–prey system with linear harvesting. Chaos, Solitons & Fractals, 169, 113286.
    [CrossRef]   [Google Scholar]
  10. Liu, C., Zhang, Q., Zhang, X., & Duan, X. (2009). Dynamical behavior in a stage-structured differential-algebraic prey–predator model with discrete time delay and harvesting. Journal of Computational and Applied Mathematics, 231(2), 612-625.
    [CrossRef]   [Google Scholar]
  11. Zhang, G., Zhu, L., & Chen, B. (2010). Hopf bifurcation and stability for a differential-algebraic biological economic system. Applied Mathematics and Computation, 217(1), 330-338.
    [CrossRef]   [Google Scholar]
  12. Li, M., Chen, B., & Ye, H. (2017). A bioeconomic differential algebraic predator–prey model with nonlinear prey harvesting. Applied Mathematical Modelling, 42, 17-28.
    [CrossRef]   [Google Scholar]
  13. Liu, W. (2026). Delayed predator-prey dynamics with Holling type IV functional response and rational nonlinear harvesting. Electronic Research Archive, 34(1), 627-656.
    [CrossRef]   [Google Scholar]
  14. Beardmore, R., & Webster, K. (2008). Normal forms, quasi-invariant manifolds, and bifurcations of nonlinear difference-algebraic equations. SIAM journal on mathematical analysis, 40(1), 413-441.
    [CrossRef]   [Google Scholar]
  15. Wiggins, S. (2003). Introduction to applied nonlinear dynamical systems and chaos. Springer-Verlag.
    [CrossRef]   [Google Scholar]
  16. Xiao, D., & Jennings, L. S. (2005). Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting. SIAM Journal on Applied Mathematics, 65(3), 737-753.
    [CrossRef]   [Google Scholar]
Cite This Article
APA Style
Han, J., & Liu, W. (2026). Bifurcation and Stability Analysis for a Class of Discrete Singular Predator-Prey System. Journal of Nonlinear Dynamics and Applications, 2(1), 39–46. https://doi.org/10.62762/JNDA.2026.505976
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TY  - JOUR
AU  - Han, Jing
AU  - Liu, Wei
PY  - 2026
DA  - 2026/03/07
TI  - Bifurcation and Stability Analysis for a Class of Discrete Singular Predator-Prey System
JO  - Journal of Nonlinear Dynamics and Applications
T2  - Journal of Nonlinear Dynamics and Applications
JF  - Journal of Nonlinear Dynamics and Applications
VL  - 2
IS  - 1
SP  - 39
EP  - 46
DO  - 10.62762/JNDA.2026.505976
UR  - https://www.icck.org/article/abs/JNDA.2026.505976
KW  - stability
KW  - neimark-Sacker bifurcation
KW  - predator-prey
KW  - discrete-time
KW  - singular system
AB  - A kind of discrete-time singular predator-prey system with time-varying harvesting term is investigated. By using theory of singular systems, bifurcation and center manifold theory, the stability and Neimark-Sacker bifurcation of such system is studied, and some conditions are used to judge local stability of its fixed points and ensure existence of the Neimark-Sacker bifurcation for the proposed discrete-time singular system are derived. Finally, numerical simulations are given to show the obtained results. The results of the paper complements some previous works, and we believe that the method of this paper can be used to study bifurcation for other discrete-time complex singular systems.
SN  - 3069-6313
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -
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@article{Han2026Bifurcatio,
  author = {Jing Han and Wei Liu},
  title = {Bifurcation and Stability Analysis for a Class of Discrete Singular Predator-Prey System},
  journal = {Journal of Nonlinear Dynamics and Applications},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {39-46},
  doi = {10.62762/JNDA.2026.505976},
  url = {https://www.icck.org/article/abs/JNDA.2026.505976},
  abstract = {A kind of discrete-time singular predator-prey system with time-varying harvesting term is investigated. By using theory of singular systems, bifurcation and center manifold theory, the stability and Neimark-Sacker bifurcation of such system is studied, and some conditions are used to judge local stability of its fixed points and ensure existence of the Neimark-Sacker bifurcation for the proposed discrete-time singular system are derived. Finally, numerical simulations are given to show the obtained results. The results of the paper complements some previous works, and we believe that the method of this paper can be used to study bifurcation for other discrete-time complex singular systems.},
  keywords = {stability, neimark-Sacker bifurcation, predator-prey, discrete-time, singular system},
  issn = {3069-6313},
  publisher = {Institute of Central Computation and Knowledge}
}
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