Background Cooperative interactions between species play a key role in ecosystem persistence, yet most predator–prey models neglect mutualistic effects between prey species. Methodology We formulate a new three-dimensional ecological model describing one predator feeding on two cooperative prey populations, modeled by a system of nonlinear ordinary differential equations. We prove the positivity and boundedness of solutions, determine all biologically meaningful equilibrium points and establish their local and global stability using linearization, Lyapunov functions and the Routh–Hurwitz criteria. We then perform a bifurcation analysis with respect to key parameters, such as natural growth, natural mortality and predator attack and conversion rates. Finally, we carry out numerical simulations in MATLAB to illustrate and complement the analytical results. Results The analysis shows that, for a realistic set of parameter values, the system admits a unique interior equilibrium that is globally asymptotically stable, and no periodic dynamics are observed. Variations in the growth rates of both prey, the predator mortality rate and the attack and conversion rates can shift the stability of equilibria and generate transcritical bifurcations. The cooperative interaction between the two prey populations enlarges the parameter region that ensures coexistence and improves the long-term persistence of all species. Numerical simulations confirm the analytical predictions and visualize the trajectories converging to the stable equilibrium. Conclusions The proposed model clarifies how mutualistic interactions among prey species can stabilize predator–prey systems and enhance ecosystem sustainability. The theoretical framework and numerical results may be used as a reference for further ecological modeling that incorporates cooperation, harvesting or environmental disturbances.
Haider Ghanem Sufaeh (Mon,) studied this question.