On the global stability of periodic Ricker maps

Abstract

We find the exact region of global stability for the $2$-periodic Ricker difference equation, showing that a $2$-periodic solution is globally asymptotically stable whenever it is locally asymptotically stable and the equation does not have more $2$-periodic solutions. We conjecture that this property holds for the general $p$-periodic Ricker difference equation, and in particular we prove it for $p=3$.

Keywords

• periodic ricker map
• difference equations
• global stability