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.
基金
This work was supported by the Higher Education Cominission of Pakistan.
