DOI: 10.1137/25m1814347 ISSN: 1536-0040

Spatially inhomogeneous two-cycles in an integrodifference equation

Kevin Church, Kevin Constantineau, Jean-Philippe Lessard
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Abstract.

In this work, we prove the existence of a two-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two nontrivial fixed points of the second iterate of the logistic map in the nonchaotic regime. This model was first studied by Kot (1992), and the two-cycle we establish qualitatively resembles one numerically observed by Bourgeois, Leblanc, and Lutscher (2018) for the Ricker growth function. Finally, we present numerical results indicating that this two-cycle exhibits spectral stability.

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