Dynamics of a non-autonomous competitive system under simultaneous impulsive pollution and anthropogenic disturbances

Lin Xiao; Haokun Qi; Yanchao Qi; Bing Liu; Lin Xiao; Haokun Qi; Yanchao Qi; Bing Liu

doi:10.3934/era.2026166

Electronic Research Archive

2026, Volume 34, Issue 6: 3678-3695. doi: 10.3934/era.2026166

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Dynamics of a non-autonomous competitive system under simultaneous impulsive pollution and anthropogenic disturbances

1.
School of Mathematics, Anshan Normal University, Liaoning 114007, China
2.
Yantai Nanshan Donghai Foreign Language School, Shandong 265700, China

Received: 04 February 2026 Revised: 15 April 2026 Accepted: 23 April 2026 Published: 30 April 2026

In this paper, the permanence and extinction of a class of non-autonomous competitive population systems existing in an impulsively polluted environment are investigated. By establishing a time-varying differential equation model that couples population competition, pollutant dynamics, and discrete impulsive disturbances, we employ the comparison theorem of impulsive differential equations and analytical methods to derive sufficient criteria guaranteeing population persistence and global extinction. Furthermore, by constructing a Lyapunov function, we obtain conditions for the global attractivity of the system solutions. The theoretical analysis indicates that the ultimate fate of the population is jointly determined by the time-varying growth rates, competition intensities, period of impulsive disturbances, and pollutant toxicity levels. This study provides a quantitative theoretical basis for assessing the ecological risks of sporadic pollution events in competitive communities.
- non-autonomous competitive population system,
- impulsive effect,
- permanence,
- extinction,
- global attractivity
Citation: Lin Xiao, Haokun Qi, Yanchao Qi, Bing Liu. Dynamics of a non-autonomous competitive system under simultaneous impulsive pollution and anthropogenic disturbances[J]. Electronic Research Archive, 2026, 34(6): 3678-3695. doi: 10.3934/era.2026166

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Abstract

In this paper, the permanence and extinction of a class of non-autonomous competitive population systems existing in an impulsively polluted environment are investigated. By establishing a time-varying differential equation model that couples population competition, pollutant dynamics, and discrete impulsive disturbances, we employ the comparison theorem of impulsive differential equations and analytical methods to derive sufficient criteria guaranteeing population persistence and global extinction. Furthermore, by constructing a Lyapunov function, we obtain conditions for the global attractivity of the system solutions. The theoretical analysis indicates that the ultimate fate of the population is jointly determined by the time-varying growth rates, competition intensities, period of impulsive disturbances, and pollutant toxicity levels. This study provides a quantitative theoretical basis for assessing the ecological risks of sporadic pollution events in competitive communities.

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