1
Department of Basic science, Hashtgerd Branch, Islamic Azad University, Alborz, Iran
2
Department of Mathematics, Alzahra university, Tehran, Iran
Abstract
This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is not more of fractional order, exhibits much richer dynamical behavior than its corresponding fractional order model. Specially, in the discretized system, many types of bifurcations (transcritical, flip, Neimark-Sacker) and chaos may happen, however, the local analysis of the fractional-order counterpart, only deals with the stability (unstability) of the equilibria. Finally, some numerical simulations are performed by MATLAB, to support our analytic results.
Shafeii Lashkarian, R., & Behmardi Sharifabad, D. (2018). Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos. Computational Methods for Differential Equations, 6(2), 248-265.
MLA
Razie Shafeii Lashkarian; Dariush Behmardi Sharifabad. "Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos". Computational Methods for Differential Equations, 6, 2, 2018, 248-265.
HARVARD
Shafeii Lashkarian, R., Behmardi Sharifabad, D. (2018). 'Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos', Computational Methods for Differential Equations, 6(2), pp. 248-265.
VANCOUVER
Shafeii Lashkarian, R., Behmardi Sharifabad, D. Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos. Computational Methods for Differential Equations, 2018; 6(2): 248-265.
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