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.

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 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.

Survival analysis of a stochastic single-species population model with jumps in a polluted environment

2015 ◽  
Vol 09 (01) ◽  
pp. 1650011 ◽  
Author(s):  
Meng Liu ◽  
Ke Wang
Keyword(s):  
Population Model ◽  
Sufficient Conditions ◽  
Single Species ◽  
Polluted Environment ◽  
Stochastic Permanence ◽  
Persistence In The Mean ◽  
Species Population ◽  
The Mean ◽  
Single Species Population ◽  
Lévy Jumps

This paper is concerned with a stochastic single-species system with Lévy jumps in a polluted environment. Some sufficient conditions on extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean, stability in the mean and stochastic permanence are obtained. The threshold between extinction and weak persistence in the mean is established. At the same time, under a simple condition, it is proved that this threshold also is the threshold between extinction and stability in the mean. The results reveal that Lévy jumps have significant effects to the persistence and extinction results.

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.

scholarly journals Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ronghua Tan ◽  
Zuxiong Li ◽  
Shengliang Guo ◽  
Zhijun Liu
Keyword(s):  
Lyapunov Functions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Single Species ◽  
Different Types ◽  
Species Population ◽  
Impulsive Perturbations ◽  
Single Species Population ◽  
Single Species Model

This is a continuation of the work of Tan et al. (2012). In this paper a periodic single species model controlled by constant impulsive perturbation is investigated. The constant impulse is realized at fixed moments of time. With the help of the comparison theorem of impulsive differential equations and Lyapunov functions, sufficient conditions for the permanence and global attractivity are established, respectively. Also, by comparing the above results with corresponding known results of Tan et al. (2012) (i.e., the above model with linear impulsive perturbations), we find that the two different types of impulsive perturbations have influence on the above dynamics. Numerical simulations are presented to substantiate our analytical results.

Sign in / Sign up

Export Citation Format

Share Document