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All Journal JPMS (Jurnal Pendidikan Matematika dan Sains) dCartesian: Jurnal Matematika dan Aplikasi Jurnal Ilmu Dasar Jurnal Gaussian CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Didaktik Matematika Jurnal Karya Pendidikan Matematika Jurnal Daya Matematis PYTHAGORAS: Jurnal Program Studi Pendidikan Matematika AKSIOMA HISTOGRAM: Jurnal Pendidikan Matematika AL ISHLAH Jurnal Pendidikan JURNAL PENDIDIKAN GLASSER BAREKENG: Jurnal Ilmu Matematika dan Terapan Jambura Journal of Mathematics Laplace : Jurnal Pendidikan Matematika ESTIMASI: Journal of Statistics and Its Application Jurnal Statistika dan Aplikasinya Jambura Journal of Mathematics Education JAMBURA JOURNAL OF PROBABILITY AND STATISTICS Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Dikmas: Jurnal Pendidikan Masyarakat dan Pengabdian MATHunesa: Jurnal Ilmiah Matematika Research in the Mathematical and Natural Sciences Jurnal Riset Mahasiswa Matematika Journal of Mathematics, Computation and Statistics (JMATHCOS) d'Cartesian: Jurnal Matematika dan Aplikasi KAMBIK : Journal of Mathematics Education
Ismail Djakaria
Universitas Negeri Gorontalo
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Environmental Science Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Journal : CAUCHY: Jurnal Matematika Murni dan Aplikasi

 1 
Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior Djakaria, Ismail; Gaib, Muhammad Bachtiar; Resmawan, Resmawan
CAUCHY Vol 6, No 4 (2021): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v6i4.11472

Abstract

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.
Co-Authors Agustina, Melisa Agusyarif Rezka Nuha Alamri, Fahima Amalia Tatu Armayani Arsal Armin Haluti Arwildayanto, Arwildayanto Asriadi Asriadi Boby Rantow Payu Caicy Magelo Demas Novaleda Abdul Karim Dewi Rahmawati Isa Dewi Rahmawaty Isa Djibran, Fahrudin Djihad Wungguli Evi Hulukati Fatmawati Payopo Fenly B Mohamad Fitra Reza Dj Wares Franky Alfrits Oroh Gaib, Muhammad Bachtiar Hamila Hulihulis Hamza B Uno HARIYATI H. USMAN Harun, Trieke Nurfadilah Haryati Octaviani Bempah Hasan, Irsan K. Hasan, Riyanto Hasan, Salmiaty HASIRU, LISA SYAHRIA Hendra Andrianto Yusuf Herlina Jusuf Isran K Hasan Iyohu, Lisa Rianti Jackonias Sanadi Jenny Patricia Ayu Kai K. Hasan, Isran K. Nasib, Salmun Kartin Usman Kasim, Miranti H. La Ode Nashar Ladjali, Nurjana Namko Ladjali, Sri Indriani Lailany Yahya Madonsa, Muhammad Rifai Mahajani, Roy Mahmud, Sri Lestari Majid Majid Majid, Majid Marice Awairaro Mentari Rizki Sawitri Pilomonu Modeong, Fakhira Mohamad Rivaldi Moha Mokoginta, Karmila Muhammad Fathurrahman Muhammad Fathurrahman Muhammad Rezky F. Payu Nazmi Al-lahmadi Ningsih, Setia NISKY IMANSYAH YAHYA Nosva Adam Yunus Novianty Djapri Nurhayati Abbas Nursiya Bito Pakaya, Debyyansa Paputungan, Arsiullahnur R. Perry Zakaria POMALINGO, DEWI ZULYANI Putri Dini Retno Pratiwi Rahmi Moh. Amin Resmawan Resmawan Ria Kilala Safrudin Ismail Salima Silayar Salmun K. Nasib Sarira, Regina Amelia siswanto, Navira Siti Nurmardia Abdussamad Sitra Kalauw Sri Endang Saleh Sri Haryatmi Kartiko Suhardiman Darson Tamu Suleman, Alis Sumarno Ismail suryo Guritno Swasti Maharani Syafrudin Katili Syafrudin, Marisa Syamsu Qomar Badu Ukhti Nurfajriah Sasmita Ijonu Ulopo, Asrul S WA SALMI WD Rifqah Amalliah Ndangi Yamin Ismail Yenni Sauli Yunus, Silvani Yusuf, Hendra Andrianto Zulkifli Alamtaha