Bifurcations and chaos control in a discrete-time biological model

• 作者: A.Q.Khan T.Khalique
• 来源期刊: 生物数学学报:英文版
• 学科: 数学
• 关键词: Lotka-Volterra model bifurcations and chaos center manifold theorem numerical simulation
• 年，卷（期）: 2020,（4）
• 页码范围: 1-31
• 页数: 31页
• 分类号: O17

摘要

In this papcr,bifurcations and chaos control in a discrete-time Lotka-Volterra predator-prey model have been studied in quadrant-I.It 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>d.By Linearization method,we explored the local dynamics along with different topological classifications about equilibria.We also explored the boundedness of positive solution,global dynamics,and existence of prime-period and periodic points of the model.It 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 appears.From the perspective of biology,these curves imply that betwecn predator and prey populations,there exist periodic or quasi-periodic oscillations.Some 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 23.The Maximum Lyapunov exponents as well as fractal dimension are computed numeri-cally to justify the chaotic behaviors in the model.Finally,feedback control method is applied to stabilize chaos existing in the model.