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Title: Complex Dynamics of a Discrete-Time Prey-Predator System with Leslie Type: Stability, Bifurcation Analyses and Chaos
Authors: Baydemir, Pınar
Merdan, Hüseyin
Karaoğlu, Esra
Sucu, Gökçe
Keywords: Chaotic behavior
Neimark–Sacker bifurcation
flip bifurcation
stability analysis
difference equation
Issue Date: Aug-2020
Publisher: World Scientific
Source: Baydemir, P., Merdan, H., Karaoglu, E., & Sucu, G. (2020). Complex Dynamics of a Discrete-Time Prey–Predator System with Leslie Type: Stability, Bifurcation Analyses and Chaos. International Journal of Bifurcation and Chaos, 30(10), 2050149.
Abstract: Dynamic behavior of a discrete-Time prey-predator system with Leslie type is analyzed. The discrete mathematical model was obtained by applying the forward Euler scheme to its continuous-Time counterpart. First, the local stability conditions of equilibrium point of this system are determined. Then, the conditions of existence for flip bifurcation and Neimark-Sacker bifurcation arising from this positive equilibrium point are investigated. More specifically, by choosing integral step size as a bifurcation parameter, these bifurcations are driven via center manifold theorem and normal form theory. Finally, numerical simulations are performed to support and extend the theoretical results. Analytical results show that an integral step size has a significant role on the dynamics of a discrete system. Numerical simulations support that enlarging the integral step size causes chaotic behavior.
ISSN: 0218-1274
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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