Global Dynamics of Three Anticompetitive Systems of Difference Equations in the Plane

Abstract EN

We investigate the global dynamics of several anticompetitive systems of rational difference equations which are special cases of general linear fractional system of the forms xn+1=(α1+β1xn+γ1yn)/(A1+B1xn+C1yn),yn+1=(α2+β2xn+γ2yn)/(A2+B2xn+C2yn),n=0,1,..., where all parameters and the initial conditions x0,y0 are arbitrary nonnegative numbers, such that both denominators are positive.

We find the basins of attraction of all attractors of these systems.