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Local stability implies global stability for the 2dimensional Ricker map
 J. Difference Equations and Applications
"... Consider the difference equation xk+1 = xkeα−xn−d where α is a positive parameter and d is a nonnegative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d ≥ 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilib ..."
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Consider the difference equation xk+1 = xkeα−xn−d where α is a positive parameter and d is a nonnegative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d ≥ 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilibrium implies its global stability. Based on rigorous, computer aided calculations and analytical tools, we prove the conjecture for d = 1.
Global Attractivity in Nonlinear Higher Order Difference Equations in Banach Algebras
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