Local and global stability analysis of a two prey one predator model with help

• Three team consist of two preys and one predator with different predation rates.
• We have done local and global stability analysis.
• Strength of competition among the individuals of prey plays an important role in determining the stability behaviour.
• Initially the population of prey species increases in the case of model with help and decreases for the model without help.

In this paper we propose and study a three dimensional continuous time dynamical system modelling a three team consists of two preys and one predator with the assumption that during predation the members of both teams of preys help each other and the rate of predation of both teams are different. In this work we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functional. At the end, numerical simulations are performed to substantiate our analytical findings.