Bifurcations and chaos control in a discrete-time biological model

作     者：A.Q.Khan T.Khalique 

作者机构：Department of Mathematics University of Azad Jammu and Kashmir Muzaffarabad 13100Pakistan 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2020年第13卷第4期

页      面：1-31页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：This work was supported by the Higher Education Cominission of Pakistan 

主　　题：Lotka-Volterra model bifurcations and chaos center manifold theorem numerical simulation 

摘      要：In this papcr,bifurcations and chaos control in a discrete-time Lotka-Volterra predator-prey model have been studied in *** is shown that for all parametric values,model hus boundary equilibria:P00(0,0),Px0(1,0),and the unique positive equilibrium point:P^+xy(d/c,r(c-d)/bc) if c*** Linearization method,we explored the local dynamics along with different topological classifications about *** also explored the boundedness of positive solution,global dynamics,and existence of prime-period and periodic points of the *** is explored that flip bifurcation occurs about boundary equilibria:Poo(0,0),P.o(1,0),and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of P^+xy(d/c,r(c-d)/bc).Further,it is also explored that about P^+xy(d/c,r(c-d)/bc) the model undergoes a N-S bifurcation,and meanwhile a stable close invariant curves *** the perspective of biology,these curves imply that betwecn predator and prey populations,there exist periodic or quasi-periodic *** simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and *** Maximum Lyapunov exponents as well as fractal dimension are computed numeri-cally to justify the chaotic behaviors in the ***,feedback control method is applied to stabilize chaos existing in the model.