PERSISTENCE AND EXTINCTION OF A STOCHASTIC SINGLE-SPECIES POPULATION MODEL IN A POLLUTED ENVIRONMENT WITH IMPULSIVE TOXICANT INPUT

2012 ◽  
Author(s):  
MENG LIU ◽  
KE WANG
Keyword(s):  
Population Model ◽  
Single Species ◽  
Polluted Environment ◽  
Species Population ◽  
Single Species Population

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.

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 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
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