Effects of diffusion on a stage-structured population in a polluted environment

Duan, Lixia; Lu, Qishao; Yang, Zaizhong; Chen, Lansun

doi:10.1016/s0096-3003(03)00713-6

Cited by 11 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, the impacts of polluted environment on the population dynamics have been investigated by several researchers. [1][2][3][4][5][6][7][8][9][10][11][12] Wei et al 2 proposed a stochastic single-species population model in a polluted environment and discussed weak persistence and permanence of the stochastic model's solution. He et al 4 presented a model to study the long-term behaviors of a population in a polluted environment and obtained the sufficient criteria for persistence or extinction of the population.…”

Section: Introductionmentioning

confidence: 99%

“…It is necessary to investigate that the dynamics of the system states (in particular population dynamics) are affected by the polluted environment when contaminant concentrations vary. Recently, the impacts of polluted environment on the population dynamics have been investigated by several researchers 1–12 . Wei et al 2 proposed a stochastic single‐species population model in a polluted environment and discussed weak persistence and permanence of the stochastic model's solution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A periodic averaging method for impulsive stochastic age‐structured population model in a polluted environment

Zhang

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we present a periodic averaging (PA) method for impulsive stochastic age‐structured population model (ISASPM) in a polluted environment. By using Young's inequality and Gronwall's lemma and under the stochastic Lipschitz condition, we reveal that both the standard ISASPM and the averaged ISASPM have a unique solution. We also study the mean‐square convergence criteria of the numerical solutions produced by the PA method. Finally, asimulation example is given to demonstrate that the PA method is efficient for our results.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A periodic averaging method for impulsive stochastic age‐structured population model in a polluted environment

Zhang

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…There are also experimental evidences (Carpenter et al, 2011) that environmental noises can play a key role in ecological systems. Given this, stochastic dynamical modelling, which is one of the powerful tools to investigate the effect of noise and toxicant on the population in a polluted environment, has attracted many researchers interests (Hallam et al, 1983;Hallam and Ma, 1986;Duan et al, 2004;Yang et al, 2007;Liu and Wang, 2009). On the other hand, due to the nature of Gaussian white noise, we need to consider another noise to reflect phenomena in ecosystems suffering switch abruptly to a contrasting alternative stable state (Scheffer et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution and ergodicity of a stochastic single-species model under regime switching in a polluted environment

Zhao

Zhai

2020

IJCSM

View full text Add to dashboard Cite

The long-term statistical rule is one of the important questions for stochastic pollution-population dynamical models, thus it would be worth looking for the stationary distribution as an indicator in analysing the effects of toxicant and noises on the variation of population in evolution process. In present paper, we investigate a stochastic single-species model under regime switching in a polluted environment. By use of the ergodic of Markov chain and constructing Lyapunov function, the sufficient conditions for the positive recurrence and ergodic property are established, which imply the existence of stationary distribution of the model. Moreover, the mean and variance of marginal stationary distribution are estimated. Our analysis indicates that the coloured noise and toxicant may play an important role in determining the shape of stationary distribution and its statistics characteristics. Finally, numerical simulations are carried out to support our theoretical results.

show abstract

Survival and Stationary Distribution Analysis of a Stochastic Competitive Model of Three Species in a Polluted Environment

2015

View full text Add to dashboard Cite

In this paper, we develop and study a stochastic model for the competition of three species with a generalized dose-response function in a polluted environment. We first carry out the survival analysis and obtain sufficient conditions for the extinction, non-persistence, weak persistence in the mean, strong persistence in the mean and stochastic permanence. The threshold between weak persistence in the mean and extinction is established for each species. Then, using Hasminskii's methods and a Lyapunov function, we derive sufficient conditions for the existence of stationary distribution for each population. Numerical simulations are carried out to support our theoretical results, and some biological significance is presented.

show abstract

Effects of diffusion on a stage-structured population in a polluted environment

Cited by 11 publications

References 11 publications

A periodic averaging method for impulsive stochastic age‐structured population model in a polluted environment

A periodic averaging method for impulsive stochastic age‐structured population model in a polluted environment

Stationary distribution and ergodicity of a stochastic single-species model under regime switching in a polluted environment

Survival and Stationary Distribution Analysis of a Stochastic Competitive Model of Three Species in a Polluted Environment

Contact Info

Product

Resources

About