Analisis Bifurkasi Hopd pada Sistem Eko-Epidemiologi

Putriliana, Dita (2017) Analisis Bifurkasi Hopd pada Sistem Eko-Epidemiologi. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Eko-epidemiologi merupakan ilmu yang mempelajari suatu penyebaran penyakit yang terjadi dalam sistem predator-prey. Umumnya sebuah sistem predator-prey mempunyai orbit periodik, sehingga dengan adanya orbit periodik dapat diidentifikasi eksistensi bifurkasi Hopf pada sistem tersebut. Pada Tugas Akhir ini dikaji mengenai sistem eko-epidemiologi dengan respon fungsional Holling tipe II dengan mencari titik kesetimbangan, kestabilan lokal titik kesetimbangan, dan eksistensi bifurkasi Hopf. Kestabilan non trivial dianalisis dengan menggunakan kriteria Routh-Hurwitz. Bifurkasi Hopf terjadi pada titik kesetimbangan dan Hasil analisis menunjukkan adanya bifurkasi Hopf yang mengelilingi titik kesetimbangan positif ketika . Untuk mendukung hasil analisis dilakukan simulasi numerik dengan menggunakan Runge-Kutta orde empat. ================================================================= Eco-epidemiology is a science of a disease spread that studies about disease transmission that occurs in predator-prey system. Generally, a predator-prey system has a periodic orbit, so that in the presence of a periodic orbit can be identified the existence of Hopf bifurcation in the system. This reaserch reviewed about eco-epidemiological system with type II of Holling functional response by finding equilibrium point, local stability of equilibrium point, and the existence of Hopf bifurcation. Non trivial stability is analysed by using Routh-Hurwitz criterion. Hopf bifurcation occurrsat the equilibrium point and The result of the analysis shows that there is a Hopf bifurcation that surrounds the positive equilibrium point when . To support the result of the analysis, a numerical simulation is performed by using the Runge-Kutta 4th order.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Model eko-epidemologi, respon fungsional, bifurkasi Hopf, Runge-Kutta orde 4, eco-epidemiological model, functional response, Hopf bifurcation, Runge-Kutta orde 4
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Mathematics and Science > Mathematics > (S1) Undergraduate Theses
Depositing User: Dita Putriliana .
Date Deposited: 16 Oct 2017 02:05
Last Modified: 08 Mar 2019 04:10
URI: http://repository.its.ac.id/id/eprint/44461

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