A conjecture on the stability of the periodic solutions of Ricker's equation with periodic parameters

In this work, we propose a conjecture about the stability of the periodic solutions of the Ricker equation with periodic parameters, which goes beyond the existing theory, and for the special case of period-two parameters we analytically show the conjecture is true. For this case we show that the stability region in parameter space obtained from the conjecture is larger than a previously proposed stability region. The period-three case is investigated numerically and similar extensions are realized. This suggests that the current theory cited in this paper, while giving sufficient conditions for stability is far from optimal. (C) 2010 Elsevier Inc. All rights reserved.