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In this paper, we investigate so-called forced wave solutions of a threecomponents reaction-diffusion system from population dynamics. Our systeminvolves three species that are respectively two competing preys and onepredator; moreover, the competition between both preys is strong, i.e. in theabsence of the predator, one prey is driven to extinction and the othersurvives. Furthermore, our problem includes a spatio-temporal heterogeneity ina moving variable that typically stands as a model for climate shift. In thiscontext, forced waves are special stationary solutions which are expected todescribe the large-time behavior of solutions, and in particular to providecriteria on the climate shift speed to allow survival of either of the threespecies. We will consider several types of forced waves to deal with varioussituations depending on which species are indigenous and which species areaboriginal.

Forced waves of a three species predator-prey system with a pair of weak-strong competing preys in a shifting environment