Investigates periodic traveling waves in integro-difference equations, suggesting implications for population dynamics.
We derive sufficient conditions for the existence of a periodic traveling wave solution to an integro-difference equation with a piecewise constant growth function exhibiting a stable period- 2 2 cycle and strong Allee effect. The mean traveling wave speed is shown to be the asymptotic spreading speed of solutions with compactly supported initial data under appropriate conditions. We then conduct case studies for the Laplace kernel and uniform kernel.
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Nestor et al. (2026) studied this question.
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