Global dynamics of a predator, weaker prey and stronger prey system

• A prey–predator ecological system with competition is considered.
• The prey species is divided into two class namely weaker and stronger classes.
• Both intra-specific and inter-specific competitions are considered in the model.
• Existence and stability criteria of the equilibria of the system are checked.
• Numerical simulations are presented to illustrate the theoretical results.

In this paper, we propose and analyze a prey–predator system consisting of two competitive prey populations and one predator population which depends on both the prey species. We investigate the boundedness and persistence criteria of the system and existence conditions of all the possible equilibria. Further the dynamical behavior from the point of view of local and global stability at different equilibria are presented. We also determine the explicit conditions so that the system has no periodic solutions. Finally, we present some numerical examples to illustrate our analytical works.