Qualitative behavior of discrete-time Caputo-Fabrizio logistic model with Allee effect  

作　　者：Hatice Karakaya Senol Kartal ilhan Oztirk 

机构地区：[1]Department of Mathematics,Faculty of Science Erciyes University,Kayseri,Turkey [2]Department of Science and Mathematics Education Faculty of Education,Nevsehir Haci Bektas Veli University Nevsehir,Turkey [3]Kapadokya University,Nevsehir,Turkey

出　　处：《International Journal of Biomathematics》2024年第4期217-234,共18页生物数学学报（英文版）

摘　　要：The aim of this paper is to investigate the dynamic behaviors of fractional-order logistic model with Allee effects in Caputo-Fabrizio sense.First of all,we apply the two-step Adams-Bashforth scheme to discretize the fractional-order logistic differential equation and obtain the two-dimensional discrete system.The parametric conditions for local asymptotic stability of equilibrium points are obtained by Schur-Chon criterion.Moreover,we discuss the existence and direction for Neimark-Sacker bifurcations with the help of center manifold theorem and bifurcation theory.Numerical simulations are provided to illustrate theoretical discussion.It is observed that Allee effect plays an important role in stability analysis.Strong Allee effect in population enhances the stability of the coexisting steady state.In additional,the effect of fractional-order derivative on dynamic behavior of the system is also investigated.

关 键 词：Caputo-Fabrizio fractional derivative two-step Adams-Basforth method logistic differential equation Neimark-Sacker bifurcation Allee effect 

分 类 号：O17[理学—数学]