Abstract
We study a non-compact version of the carrying simplex for the planar Leslie–Gower and planar Ricker maps when they are written in logarithmic variables. We show that for both of these models there is a convex (unbounded) invariant set X ∞ , and all orbits are attracted to X ∞ . For the Leslie–Gower map, which is injective, the boundary of X ∞ globally attracts all orbits and we identify it with a non-compact carrying simplex. As the Ricker map is not invertible, the boundary of X ∞ may not be invariant. We establish conditions on the parameters of the Ricker map which guarantee that there is a convex non-compact carrying simplex when r, s<1 which maps into a compact carrying simplex in the standard untransformed coordinates.
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