Theoretical and semi-analytical simulation for a two-predator-one-prey model during the mating period

The article introduces a new application which is a system of equations of two predators and one prey with the term of interaction between male and female of predators and prey. Such term appears when male and female of predators feed on the same prey during their mating period. The mathematical model has been studied theoretically and semi-analytically. The positivity, boundedness, local and global stability are proved for the system. The logarithm of multistage differential transform method (MsDTM) is used to study this new application. The MsDTM is used because it globally converges to the solution, it is a highly accurate, fast and simple approach. The stability analysis as well as semi-analytical solutions of the system are obtained to understand the dynamic of the model. Moreover, the effects of several parameters in the system are presented. As a results, we obtain the periodic solution when when the growth rate of prey is larger than the growth rate of both type of predators.