Analisis Dinamik Skema Euler Untuk Model Predator-Prey Dengan Efek Allee Kuadratik

Vivi Aida Fitria
S. Nurul Afiyah

Abstract


Pada penelitian ini dilakukan pendekatan numerik menggunakan skema Euler pada model predator-prey dengan efek alelopati. Perilaku dinamik dari model diskrit yang diperoleh kemudian dianalisis, yaitu eksistensi dan kestabilan titik kesetimbangan model tersebut. Analisis kestabilan titik kesetimbangan menunjukkan bahwa titik kepunahan predator dan predator-prey bersifat tidak stabil tetapi titik kepunahan prey dan titik keberhasilan hidup predator-prey bersifat stabil dengan syarat tertentu. Dari simulasi numerik menunjukkan bahwa hasil yang diperoleh sesuai dengan hasil analisis.

Keywords


Model diskrit Predator-prey; Efek alelopati; Kestabilan

References


Agiza, H. N., Elabbasy, E. M., El-Metwally, H., & Elsadany, A. A. (2009). Chaotic dynamics of a discrete prey–predator model with Holling type II. Nonlinear Analysis: Real World Applications, 10(1), 116-129.

Bandyopadhyay, M., Saha, T., & Pal, R. (2008). Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment. Nonlinear Analysis: Hybrid systems, 2(3), 958-970.

Fayeldi, T. (2013). Perilaku dinamik model epidemi sir diskrit dengan tingkat kejadian infeksi nonmonoton. Tesis. Universitas Brawijaya.

Fitria. (2015). Stability analysis of predator-prey model with allelopathic effect. AIP Conference Proceedings, 1651(59), 59-63.

Jie, W., Xi-Sheng, Z., Xian-He, Z., & Hong-Liang, G. (2012). Stability and Hopf Bifurcation Analysis on a Numerical Discretization of the Distributed Delay Equation. Chinese Physics Letters, 29(5), 050203.

Liu, X., & Xiao, D. (2007). Complex dynamic behaviors of a discrete-time predator–prey system. Chaos, Solitons & Fractals, 32(1), 80-94.

Murray, J. D. (2002). Mathematical Biology I: An Introduction Third Edition. Springer. Verlag Berlin Heidelberg.

Naji, R.K & A.H. Lafta. (2013). On the dynamics of discrete-time prey-predator system with ratio-dependent functional response. Iraqi Journal of Science, 54(1), 157-164.

Rice, E. (1984). Allelopathy. New York: Academic Press.

Wang, W. X., Zhang, Y. B., & Liu, C. Z. (2011). Analysis of a discrete-time predator–prey system with Allee effect. Ecological Complexity, 8(1), 81-85.

Wang, X., Liu, H., & Xu, C. (2012). Hopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay. Nonlinear Dynamics, 69(4), 2155-2167.

Wu, R., & Li, L. (2009). Permanence and global attractivity of discrete predator-prey system with Hassell-Varley type functional response. Discrete Dynamics in Nature and Society, 2009.




DOI: https://doi.org/10.26594/jmpm.v2i1.774

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