Analysis reveals positive traveling waves in prey-predator models, indicating a relationship between predator survival and prey density.
We study a singular diffusive prey-predator system with nonlocal dispersal for which the carrying capacity of the predator is proportional to the density of prey. We show the existence of positive one-dimensional traveling waves connecting the predator-free state and the constant co-existence state. The set of admissible wave speeds is proved to be equal to the semi-infinite interval [s^*,∞), for some s^*>0 which is characterized by a variational formula.
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Guo et al. (2025) studied this question.
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