This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.
This paper discusses the analysis of the Rosenzweig-MacArthur predator-prey model with anti-predator behavior. The analysis is started by determining the equilibrium points, existence, and conditions of the stability. Identifying the type of Hopf bifurcation by using the divergence criterion. It has shown that the model has three equilibrium points, i.e., the extinction of population equilibrium point (E0), the non-predatory equilibrium point (E1), and the co-existence equilibrium point (E2). The existence and stability of each equilibrium point can be shown by satisfying several conditions of parameters. The divergence criterion indicates the existence of the supercritical Hopf-bifurcation around the equilibrium point E2. Finally, our model's dynamics population is confirmed by our numerical simulations by using the 4th-order Runge-Kutta methods.
Artikel ini mengkaji model mangsa-pemangsa yang saling berkompetisi, dengan menggunakan fungsi respon Monod-Haldane dan perilaku anti pemangsa. Artikel inimembahas penentuan titik tetap, analisis kestabilan titik tetap dan simulasi numerik. Diperoleh tiga titik tetap yaitu T1, T2 dan T3 dimana kestabilan titik tetap T1 selalu bersifatsadel, kestabilan titik tetap T2 dan T3 akan stabil jika memenuhi syarat parameter yang telah ditentukan. Terdapat dua kasus dalam titik tetap T3, dimana kasus pertama bersifat simpul stabil dan kasus kedua bersifat spiral stabil
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