Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input

2012 ◽  
Vol 45 (12) ◽  
pp. 1541-1550 ◽  
Author(s):  
Meng Liu ◽  
Ke Wang
Keyword(s):  
Single Species ◽  
Random Perturbations ◽  
Polluted Environment ◽  
Population System ◽  
Species Population ◽  
Single Species Population

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 Survival analysis of single-species population diffusion models with chemotaxis in polluted environment

2020 ◽  
Vol 5 (6) ◽  
pp. 6749-6765
Author(s):  
Xiangjun Dai ◽  
◽  
Suli Wang ◽  
Baoping Yan ◽  
Zhi Mao ◽  
...  
Keyword(s):  
Survival Analysis ◽  
Single Species ◽  
Diffusion Models ◽  
Polluted Environment ◽  
Species Population ◽  
Single Species Population

A MODEL FOR THE EFFECT OF TIME DELAY ON THE DYNAMICS OF A POPULATION LIVING IN A POLLUTED ENVIRONMENT

2004 ◽  
Vol 12 (01) ◽  
pp. 35-43 ◽  
Author(s):  
B. DUBEY
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Single Species ◽  
Polluted Environment ◽  
Species Population ◽  
Single Species Population

In this paper, a mathematical model is proposed and analyzed to study the effect of time delay on the dynamics of a single-species population living in a polluted environment. It is shown that time delay in the model has destabilizing effect on the system.

scholarly journals Mathematical Analysis of a Single-Species Population Model in a Polluted Environment with Discrete Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Hopf Bifurcation ◽  
Population Model ◽  
Time Delays ◽  
Equilibrium Points ◽  
Single Species ◽  
Polluted Environment ◽  
Normal Form Theory ◽  
Species Population ◽  
The Stability ◽  
Single Species Population

We have discussed the dynamical behaviour of a single-species population model in a polluted environment which describes the effect of toxicants on ecological system. Boundedness, positivity, and stability analysis of the model at various equilibrium points is discussed thoroughly. We have also studied the effect of single discrete delay as well as double discrete delays on the population model. Existence conditions of the Hopf bifurcation for single time delay are investigated. The length of delay preserving the stability is also estimated. The direction and the stability criteria of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. The stability of the model with double time delays is investigated by using the Nyquist criteria. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a Hopf bifurcation. Some numerical simulations for justifying the theoretical results are also illustrated by using MATLAB, which shows the reliability of our model from the practical point of view.

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