Global dynamics, Neimark-Sacker bifurcation and hybrid control in a Leslie’s prey-predator model

In the present study, we explore the topological classifications at fixed points, global dynamics, Neimark-Sacker bifurcation and hybrid control in the two-dimensional discrete-time Leslie’s prey-predator model. It is proved that for all involved parameters a , b , c , d , h and α , discrete-time Leslie’s prey-predator model has boundary and interior fixed points: E x 0 ( a b , 0 ) , E xy + a α cd + b α , ad cd + b α respectively. Then by linear stability theory, local dynamics with different topological classifications are investigated at fixed points: E x 0 ( a b , 0 ) , E xy + a α cd + b α , ad cd + b α . Further for the discrete-time Leslie’s prey-predator model, existence of periodic points are also investigated. By bifurcation theory, it is also proved that if ( a , b , c , d , h , α ) ∈ NSB E xy + a α cd + b α , ad cd + b α then at interior fixed point: E xy + a α cd + b α , ad cd + b α , discrete Leslie’s prey-predator model undergo Neimark-Sacker bifurcation and no other bifurcation occurs at it. Moreover, hybrid control strategy is applied to control Neimark-Sacker bifurcation. Boundedness and global dynamics of the discrete-time Leslie’s prey-predator model are also investigated. Finally, obtained results are numerically verified.