We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of e...We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of each fixed point depending on the parameters.Finding two invariant sets of the evolution operator,we study the dynamical systems generated by the operator on each invariant set.Depending on the parameters,we classify the dynamics between a predator and a prey of the Leslie’s model.展开更多
基金Shoyimardonov thanks the El-Yurt Umidi Foundation under the Cabinet of Ministers of the Republic of Uzbekistan for financial support during his visit to the University of Montpellier(France)and Prof.R.Varro for the invitation。
文摘We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of each fixed point depending on the parameters.Finding two invariant sets of the evolution operator,we study the dynamical systems generated by the operator on each invariant set.Depending on the parameters,we classify the dynamics between a predator and a prey of the Leslie’s model.
