Dynamical analysis of an ecological aquaculture management model with stage-structure and nonlinear impulsive releases for larval predators

Lin Wu; Jianjun Jiao; Xiangjun Dai; Zeli Zhou; Lin Wu; Jianjun Jiao; Xiangjun Dai; Zeli Zhou

doi:10.3934/math.20241410

AIMS Mathematics

2024, Volume 9, Issue 10: 29053-29075. doi: 10.3934/math.20241410

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Research article

Dynamical analysis of an ecological aquaculture management model with stage-structure and nonlinear impulsive releases for larval predators

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
2.
School of Date Science, Tongren University, Tongren 554300, China
3.
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Received: 28 June 2024 Revised: 13 August 2024 Accepted: 30 August 2024 Published: 14 October 2024
MSC : 34A37, 35J55, 37M05, 92D25

Ecological aquaculture represents an important approach for maintaining sustainable economic income. Unreasonable aquaculture may result in resource wastage and population extinction. Human activities and behaviors such as predation among populations make the ecosystem very complex. Thus, seeking an appropriate intervention strategy is a favorable measure to overcome this situation. In this paper, we present a novel ecological aquaculture management model with stage-structure and impulsive nonlinear releasing larval predators. The sufficient conditions for the prey and the predators coexistence as well as global stability of a prey-vanishing periodic solution were obtained using the Floquet theorem and other analytic tactics. Subsequently, we verified our findings using mathematical software. We also found a system with a nonlinear impulse exhibiting rich dynamical properties by drawing bifurcation parameter graphs. These findings provide a firm theoretical basis for managing ecological aquaculture.
- ecological aquaculture,
- nonlinear impulsive release,
- stage-structure,
- extinction,
- permanence
Citation: Lin Wu, Jianjun Jiao, Xiangjun Dai, Zeli Zhou. Dynamical analysis of an ecological aquaculture management model with stage-structure and nonlinear impulsive releases for larval predators[J]. AIMS Mathematics, 2024, 9(10): 29053-29075. doi: 10.3934/math.20241410

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Abstract

Ecological aquaculture represents an important approach for maintaining sustainable economic income. Unreasonable aquaculture may result in resource wastage and population extinction. Human activities and behaviors such as predation among populations make the ecosystem very complex. Thus, seeking an appropriate intervention strategy is a favorable measure to overcome this situation. In this paper, we present a novel ecological aquaculture management model with stage-structure and impulsive nonlinear releasing larval predators. The sufficient conditions for the prey and the predators coexistence as well as global stability of a prey-vanishing periodic solution were obtained using the Floquet theorem and other analytic tactics. Subsequently, we verified our findings using mathematical software. We also found a system with a nonlinear impulse exhibiting rich dynamical properties by drawing bifurcation parameter graphs. These findings provide a firm theoretical basis for managing ecological aquaculture.

References

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