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.

• Type: Journal
• Year: 2010
• Where: AMC
• Authors: Robert J. Sacker, Hubertus F. von Bremen
• Keywords: AMC 2010, Conjecture, Parameter, Stability Region