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.

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.

PERMANENCE AND UNIFORMLY ASYMPTOTICAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR A SINGLE-SPECIES MODEL WITH FEEDBACK CONTROL ON TIME SCALES

2014 ◽  
Vol 07 (01) ◽  
pp. 1450004 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang ◽  
Hongtao Zhang
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Single Species ◽  
Asymptotical Stability ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniformly Asymptotical Stability ◽  
Single Species Model

In this paper, using the time scale calculus theory, we first discuss the permanence of a single-species model with feedback control on time scales. Based on the permanence result, by the Lyapunov functional method, we establish sufficient conditions for the existence and uniformly asymptotical stability of almost periodic solutions of the considered model. Moreover, we present an illustrative example to show the effectiveness of obtained results.

Average conditions for permanence and extinction in nonautonomous single-species Kolmogorov systems

2017 ◽  
Vol 10 (02) ◽  
pp. 1750028
Author(s):  
Jiandong Zhao ◽  
Zhenzhen Chen
Keyword(s):  
Global Attractivity ◽  
Single Species ◽  
Logistic Equation ◽  
Math Biol ◽  
Kolmogorov System ◽  
Generalized Logistic Equation

The nonautonomous single-species Kolmogorov system is studied in this paper. Average conditions are obtained for permanence, global attractivity and extinction in the system. Applications of our main results to logistic equation and generalized logistic equation are given. It is shown that our average conditions are improvement of those in Vance and Coddington [J. Math. Biol. 27 (1989) 491–506] and some published literature on the system.

IMPULSIVE DISPERSAL OF PLANT SEEDS IN SINGLE SPECIES MODEL

2007 ◽  
Vol 15 (03) ◽  
pp. 385-396
Author(s):  
LIMIN WANG ◽  
YUANSHUN TAN ◽  
LANSUN CHEN
Keyword(s):  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Plant Seeds ◽  
Impulsive Diffusion ◽  
Globally Stable ◽  
Natural Description ◽  
Negative Growth ◽  
Single Species Model

In this paper, a single species model with impulsive diffusion between two patches is proposed, which provides a more natural description of plant seeds dynamics compared with the continuous or discrete ones. By using the discrete dynamical system generated by a monotone, concave map for the dispersal model and a ∊1 - ∊2 variation, it is proved that the Poincare map has a globally stable positive fixed point. This implies that the system considered here has a globally stable positive periodic solution under some sufficient conditions. Further numerical simulations show that the diffusion can save the extinction though the species has a negative growth rate in one patch.

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