Periodic and Chaotic Orbits of a Discrete Rational System

Abstract EN

We study a rational planar system consisting of one linear-affine and one linear-fractionaldifference equation.

If all of the system’s parameters are positive (so that the positive quadrantis invariant and the system is continuous), then we show that the unique fixed point of thesystem in the positive quadrant cannot be repelling and the system does not have a snap-backrepeller.

By folding the system into a second-order equation, we find special cases of the systemwith some negative parameter values that do exhibit chaos in the sense of Li and Yorke withinthe positive quadrant of the plane.