To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.

为了应对我们生态系统在现实生活中的多样性，本文分析了两种猎物-双捕食者模型，包括 I 型和 II 型功能反应。计算了所提出模型的内部平衡点；并研究模型在该点附近的行为。讨论了内部平衡点的局部稳定性；并研究了可能方向的Hopf分岔的可能性。应用 Poincaré-Bendixon 准则的广义形式来建立所提议模型在内部平衡点周围的全局稳定性的充分条件。还进行了数值模拟以支持我们的工作。最后还包括我们的研究结果的结论和一些可能的未来方向。