Behzad Ghanbari

This paper presents various systems that investigate the interaction between two-population as predator-prey interaction, mutualism interaction, and competitive interaction. The most important assumption considered in the construction of models is to assume that the first population exhibit two contradictory behaviors herd behavior of some of them and solitary demeanor for the remainder density. This last category can be called by the escaped individuals from the flock. In the real world, it is almost impossible for any population to keep the group together all the time. Thus, we considered a proportional density of the herd that leaves it and goes in any direction. Further, the shape of the herd is considered in the construction of the model. The most important feature of the model is the study of the effect of the specific behavior of the first population in the interaction between the two mentioned populations. In this paper, a new and efficient numerical method is used to illustrate the effects of these two components.