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• W4382138688 abstract "A quadratic Lyapunov function is demonstrated for the non-invertible planar Ricker map (x,y)↦(xer−x−αy,yes−y−βx) which shows that for α,β>0, and 0<r,s≤2 all orbits of the planar Ricker map converge to a fixed point. We establish that for 0<r, s<2, whenever a positive equilibrium exists and is locally asymptotically stable, it is globally asymptotically stable (i.e. attracts all of (0,∞)2). Our approach bypasses and improves on methods that rely on monotonicity, which require 0<r,s≤1. We also use the Lyapunov function to identify the one-dimensional stable and unstable manifolds when the positive fixed point exists and is a hyperbolic saddle." @default.
• W4382138688 created "2023-06-27" @default.
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• W4382138688 date "2023-05-04" @default.
• W4382138688 modified "2023-09-26" @default.
• W4382138688 title "A global picture for the planar Ricker map: convergence to fixed points and identification of the stable/unstable manifolds" @default.
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• W4382138688 doi "https://doi.org/10.1080/10236198.2023.2222855" @default.
• W4382138688 hasPublicationYear "2023" @default.
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