Analisis bifurkasi Hopf-Transcritical pada model penyebaran HIV-1 = Analysis of Hopf-Transcritical bifurcation on HIV-1 infection model

Priscilla, Gabrielle (2022) Analisis bifurkasi Hopf-Transcritical pada model penyebaran HIV-1 = Analysis of Hopf-Transcritical bifurcation on HIV-1 infection model. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Bifurkasi pada sistem berguna untuk menentukan klasifikasi parameter dan memperlihatkan perilaku sistem dalam jangka panjang. Pada penelitian ini, akan dilakukan analisis klasifikasi dinamika, analisis bentuk normal bifurkasi, dan analisis bifurkasi yang muncul pada model penyebaran HIV-1 5-dimensi, menggunakan diagonalisasi dan center manifold reduction. Penelitian akan dimulai dengan mencari titik ekuilibrium dari sistem, lalu mencari bentuk normal bifurkasi dan bifurkasi yang muncul pada titik ekuilibrium berdasarkan nilai parameter bifurkasi yang dipilih. Selanjutnya, dilakukan simulasi numerik di sekitar titik ekuilibrium untuk melihat bifurkasi yang muncul dan klasifikasi dinamik sistem menggunakan MATLAB. Hasil penelitian menunjukkan bahwa bentuk normal bifurkasi yang muncul merupakan bifurkasi Transcritical dan Hopf Transcritical. Selain itu, simulasi numerik juga memperlihatkan pergerakan sistem menuju titik ekuilibrium yang stabil dan menjauh dari titik ekuilibrium yang tidak stabil, berdasarkan nilai parameter bifurkasi yang digunakan. / Bifurcation from a system can be use to determine the classification of parameters and show the system’s long-term behavior. In this study, analysis of classification of dynamic, analysis of bifurcation’s normal form and analysis of bifurcations that show up in the 5-dimension HIV-1 infection model, will be looked into using diagonalization and center manifold reduction. The study started from looking at the system’s equilibrium points, continued by looking for the bifurcation’s normal form and bifurcations that show up on the equilibrium points, depending on the bifurcation parameter picked. Later, numeric simulation is done around the equilibrium points to see bifurcations that show up in the system, and classifying the system’s dynamic using MATLAB. The study shows that there are Transcritical bifurcation’s and Hopf Transcritical bifurcation’s normal form in the system. Numeric simulation also shows that the system moves towards stable equilibrium points, and moves away from unstable equilibrium points, depending on the bifurcation parameter used.

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