Convexity of non-compact carrying simplices in logarithmic coordinates (Q6633398)

In this paper, the authors investigate the convexity properties of non-compact carrying simplices for the planar Leslie-Gower and Ricker maps in logarithmic coordinates. They demonstrate that both maps exhibit an unbounded convex invariant set \(X_\infty\), which attracts all orbits in the transformed coordinate space. In the case of the Leslie-Gower map, the boundary of \(X_\infty\) is globally attracting and serves as a unique non-compact carrying simplex. For the Ricker map, the boundary of \(X_\infty\) is not necessarily invariant due to the map's non-invertibility, but convexity is preserved in the case of \(r,s<1\).