Article

Leslie’s prey–predator model in discrete time

U. A. RozikovS. K. ShoyimardonovDepartment of Higher Mathematics, Tashkent University of Information Technologies, Named After Muhammad Al-Khwarizmi, Tashkent, Uzbekistan

International Journal of Biomathematicsjournal2020en

ABI

Abstract

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.

Topics

Mathematical and Theoretical Epidemiology and Ecology Models Advanced Differential Equations and Dynamical Systems Mathematical Biology Tumor Growth

Identifiers

DOI: 10.1142/s1793524520500539

Citations and references

Cited by 1 25 references

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