Global dynamics of certain competitive system in the plane

Abstract

The competitive system of difference equations

where parameters a, b, d, e are positive real numbers, and the initial conditions and are non-negative real numbers is considered. A complete classification of all possible dynamical behaviour scenarios according to all different parameter configurations is obtained.

Keywords:

• basin of attraction
• competitive
• map
• global stable manifold
• monotonicity
• period-two solution

Keywords:

• Primary: 37G35
• Secondary: 39A10, 39A11

Acknowledgements

The authors thank an anonymous referee for suggestions that resulted in an improved organization of this paper.