Local stability implies global stability for the 2-dimensional Ricker map
Dynamical Systems
2013-06-06 v1 Numerical Analysis
Abstract
Consider the difference equation where is a positive parameter and d is a non-negative 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.
Keywords
Cite
@article{arxiv.1209.2406,
title = {Local stability implies global stability for the 2-dimensional Ricker map},
author = {Ferenc A. Bartha and Ábel Garab and Tibor Krisztin},
journal= {arXiv preprint arXiv:1209.2406},
year = {2013}
}
Comments
for associated C++ program, mathematica worksheet and output, see http://www.math.u-szeged.hu/~krisztin/ricker