Spatially inhomogeneous two-cycles in an integrodifference equation

2025/10/24 by Church, Kevin, Constantineau, Kevin, Lessard, Jean-Philippe
#Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Functional Analysis (math.FA) #Populations and Evolution (q-bio.PE)

paper · doi:10.48550/arxiv.2510.21134

Abstract

In this work, we prove the existence of a 2-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two non-trivial fixed points of the second iterate of the logistic map in the non-chaotic regime. This model was first studied by Kot (1992), and the 2-cycle we establish corresponds to one numerically observed by Bourgeois, Leblanc, and Lutscher (2018) for the Ricker growth function. We provide strong evidence that the 2-cycle for the Ricker growth function can be rigorously proven using a similar approach. Finally, we present numerical results indicating that both 2-cycles exhibit spectral stability.

Citations

• Computer-assisted proofs for the many steady states of a chemotaxis model with local sensing
• Numerical computation of transverse homoclinic orbits for periodic solutions of delay differential equations
• A constructive proof of the Cauchy-Kovalevskaya theorem for ordinary differential equations
• Validated computations for connecting orbits in polynomial vector fields
• Discrete-time growth-dispersal models
• Discrete-time travelling waves: Ecological examples

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