EXTINCTION AND PERSISTENCE IN A LOGISTIC MODEL WITH BIRTH AND HARVESTING IMPULSES

Ying Yuan; Haiyan Xu; Zhigui Lin

doi:10.11948/20240131

2025 Volume 15 Issue 1

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Ying Yuan, Haiyan Xu, Zhigui Lin. EXTINCTION AND PERSISTENCE IN A LOGISTIC MODEL WITH BIRTH AND HARVESTING IMPULSES[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 488-501. doi: 10.11948/20240131

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Ying Yuan, Haiyan Xu, Zhigui Lin. EXTINCTION AND PERSISTENCE IN A LOGISTIC MODEL WITH BIRTH AND HARVESTING IMPULSES[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 488-501. doi: 10.11948/20240131

EXTINCTION AND PERSISTENCE IN A LOGISTIC MODEL WITH BIRTH AND HARVESTING IMPULSES

1.
School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
2.
School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Author Bio: Email: 615706707@qq.com(Y. Yuan); Email: 3266261977@qq.com(H. Xu)
Corresponding author: Email: zglin68@hotmail.com(Z. Lin)
Fund Project: The third author is supported by the National Natural Science Foundation of China (No. 12271470).

Abstract

Abstract

This paper deals with a diffusive logistic model with birth and harvesting impulses, where birth pulses are for increase of population in short time because of birth, and harvesting pulses are used to describe decrease of population by regular harvesting or interventions. Firstly, the principal eigenvalue depending the impulsive rates, which is regarded as a threshold value, is introduced and characterized. Secondly, the asymptotic behavior of population is fully investigated and the sufficient conditions for the solution to be extinct or persist are given. Our results show that the increase brought about by birth, the decrease caused by harvest, and the intervention timing all have an impact on the persistence of species.
- Logistic model /
- pulse /
- threshold value /
- persistence /
- extinction
MSC: 35K57, 35R35, 92D25

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References

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