Dynamical analysis of an aquaculture management model with stage structure, intraspecific cooperation, refuge effect, and nonlinearly impulsive releasing

Xueying Zhu; Jianjun Jiao; Lin Wu; Die Li; Xueying Zhu; Jianjun Jiao; Lin Wu; Die Li

doi:10.3934/math.2026252

AIMS Mathematics

2026, Volume 11, Issue 3: 6080-6105. doi: 10.3934/math.2026252

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Research article

Dynamical analysis of an aquaculture management model with stage structure, intraspecific cooperation, refuge effect, and nonlinearly impulsive releasing

School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Received: 14 December 2025 Revised: 05 February 2026 Accepted: 28 February 2026 Published: 11 March 2026
MSC : 34A37, 37M05, 92D25

In this paper, we propose an aquaculture management model with stage structure, intraspecific cooperation, refuge effect, and nonlinearly impulsive releasing. The global asymptotic stability of the periodic solution for the subsystem of the system was analyzed via the Jury criterion and the Banach contraction mapping principle. Additionally, through the theory of impulsive differential equations, the conditions for the global asymptotic stability of the prey-vanishing periodic solution and for the permanence of the system were acquired. Finally, numerical simulations were utilized to validate the theoretical results. In addition, key parameters affecting the persistence condition $ B_0 $ were identified via comparative and sensitivity analysis. Moreover, abundant dynamical behaviors such as period bifurcation and chaos were identified through bifurcation diagrams.
- stage structure,
- intraspecific cooperation,
- refuge effect,
- nonlinearly impulsive releasing,
- sensitivity analysis
Citation: Xueying Zhu, Jianjun Jiao, Lin Wu, Die Li. Dynamical analysis of an aquaculture management model with stage structure, intraspecific cooperation, refuge effect, and nonlinearly impulsive releasing[J]. AIMS Mathematics, 2026, 11(3): 6080-6105. doi: 10.3934/math.2026252

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Abstract

In this paper, we propose an aquaculture management model with stage structure, intraspecific cooperation, refuge effect, and nonlinearly impulsive releasing. The global asymptotic stability of the periodic solution for the subsystem of the system was analyzed via the Jury criterion and the Banach contraction mapping principle. Additionally, through the theory of impulsive differential equations, the conditions for the global asymptotic stability of the prey-vanishing periodic solution and for the permanence of the system were acquired. Finally, numerical simulations were utilized to validate the theoretical results. In addition, key parameters affecting the persistence condition $ B_0 $ were identified via comparative and sensitivity analysis. Moreover, abundant dynamical behaviors such as period bifurcation and chaos were identified through bifurcation diagrams.

References

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