scholarly journals A comment on “Mathematical study of a Leslie-Gower type tritrophic population model in a polluted environment” [Modeling in Earth Systems and Environment 2 (2016) 1–11]

2016 ◽  
Vol 2 (2) ◽  
Author(s):  
Rana D. Parshad ◽  
Said Kouachi ◽  
Nitu Kumari
Keyword(s):  
Population Model ◽  
Polluted Environment ◽  
Mathematical Study ◽  
Environment Modeling ◽  
Earth Systems

Mathematical study of fractional-order biological population model using optimal homotopy asymptotic method

2016 ◽  
Vol 09 (06) ◽  
pp. 1650081 ◽  
Author(s):  
S. Sarwar ◽  
M. A. Zahid ◽  
S. Iqbal
Keyword(s):  
Fractional Order ◽  
Asymptotic Method ◽  
Population Model ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Population Models ◽  
Mathematical Study ◽  
Third Order ◽  
Biological Population ◽  
Optimal Homotopy Asymptotic Method

In this paper, we study the fractional-order biological population models (FBPMs) with Malthusian, Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method (OHAM) for partial differential equations (PDEs) is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional-order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.

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.

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