A stage-structured single species model with pulse input in a polluted environment

2008 ◽  
Vol 57 (3) ◽  
pp. 375-382 ◽  
Author(s):  
Shaohong Cai
Keyword(s):  
Single Species ◽  
Polluted Environment ◽  
Pulse Input ◽  
Single Species Model

Permanence and extinction of a single species model in polluted environment

2020 ◽  
Vol 13 (04) ◽  
pp. 2050031
Author(s):  
Jiandong Zhao ◽  
Tonghua Zhang
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Logistic Equation ◽  
Polluted Environment ◽  
Math Model ◽  
Generalized Logistic Equation ◽  
Appl Math ◽  
Single Species Model

Under the assumption that the growth of the population satisfies the generalized logistic equation, a new single species model in polluted environment is proposed in this work. Sufficient conditions for permanence and extinction of the species in the model are given respectively. It is shown that our model and the results are improvements of those in He and Wang [Appl. Math. Model. 31 (2007) 2227–2238].

scholarly journals Dynamics of a stochastic population model with predation effects in polluted environments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Guanghai Song
Keyword(s):  
Numerical Simulations ◽  
Growth Rates ◽  
Population Model ◽  
Sufficient Conditions ◽  
Single Species ◽  
Polluted Environment ◽  
Predation Effect ◽  
Predation Effects ◽  
Stochastic Population Model ◽  
Single Species Model

AbstractThe present paper puts forward and probes a stochastic single-species model with predation effect in a polluted environment. We propose a threshold between extermination and weak persistence of the species and provide sufficient conditions for the stochastic persistence of the species. In addition, we evaluate the growth rates of the solution. Theoretical findings are expounded by some numerical simulations.

scholarly journals Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bing Liu ◽  
Shi Luan ◽  
Yinghui Gao
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Fixed Time ◽  
Polluted Environment ◽  
State Dependent ◽  
Pollution Treatment ◽  
Impulsive Model ◽  
The Given ◽  
Theoretical Results ◽  
Single Species Model

Without any question, environmental pollution is the main cause for the species extinction in recent times. In this paper, based on impulsive differential equation, the dynamics of a single-species model with impulsive pollution treatment at fixed time in a polluted environment is considered, in which we assume that the species is directly affected by the pollutants. Sufficient conditions for permanence and extinction of the species are given. The results show that the species is permanent when the impulsive period is less than some critical value, otherwise the species will be extinct. Although shortening the impulsive period can protect the species from extinction, it is expensive. To see how pollution treatment applications could be economical, we also establish a hybrid impulsive model involving periodic pollution treatment at fixed time with state-dependent pollution treatment applied when the pollution concentration reaches the given Environment Threshold (ET). It indicates that the hybrid method is the most effective method to protect the species from extinction. Numerical simulations confirm our theoretical results.

THE OPTIMAL PULSE HARVESTING POLICY ON A SINGLE-SPECIES POPULATION MODEL WITH BIRTH PULSES IN A POLLUTED ENVIRONMENT

2007 ◽  
Vol 10 (02) ◽  
pp. 173-196 ◽  
Author(s):  
BING LIU ◽  
FENGMEI TAO
Keyword(s):  
Population Model ◽  
Discrete Dynamical System ◽  
Single Species ◽  
Polluted Environment ◽  
Threshold Conditions ◽  
Period Solution ◽  
Species Population ◽  
Simulation Results ◽  
Single Species Population ◽  
Single Species Model

We investigate the dynamics of a single-species model with birth pulses and pulse harvesting in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact 1-period solution of the system whose birth function is a Ricker or Beverton–Holt function and obtain the threshold conditions for their stability. Further, we show the effects of the time of pulse harvesting on the maximum annual-sustainable yield. Our results show that the best time for harvesting is immediately after the birth pulses. Numerical simulation results also show that birth pulses and pulse harvesting make the single-species model in a polluted environment we consider more complex, and the system is dominated by periodic and chaotic solutions.

scholarly journals Survival analysis of a stochastic delay single-species system in polluted environment with psychological effect and pulse toxicant input

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiangjun Dai ◽  
Suli Wang ◽  
Weizhi Xiong ◽  
Ni Li
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Threshold Value ◽  
Psychological Effect ◽  
Polluted Environment ◽  
Population System ◽  
Stochastic Delay ◽  
Species Population ◽  
The Mean ◽  
Single Species Population

Abstract We propose and study a stochastic delay single-species population system in polluted environment with psychological effect and pulse toxicant input. We establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and strong persistence of the single-species population and obtain the threshold value between extinction and weak persistence. Finally, we confirm the efficiency of the main results by numerical simulations.

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