Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

Ayele Taye Goshu^*, Purnachandra Rao Koya

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia.

DOI: 10.4236/ojmsi.2015.33008                

Abstract

The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.

Keywords

Exponential Integral Function, Gompertz Model, Population Growth, Predator, Prey

Conflicts of Interest

The authors declare no conflicts of interest.

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