Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food

This work deals with a taxis cascade model for food consumption in two populations, namely foragers directly orienting their movement upward the gradients of food concentration and exploiters taking a parasitic strategy in search of food via tracking higher forager densities. As a consequence, the dynamics of both populations are adapted to the space distribution of food which is dynamically modified in time and space by the two populations. This model extends the classical one-species chemotaxis-consumption systems by additionally accounting for a second taxis mechanism coupled to the first in a consecutive manner. It is rigorously proved that for all suitably regular initial data, an associated Neumann-type initial-boundary value problem for the spatially one-dimensional version of this model possesses a globally defined bounded classical solution. Moreover, it is asserted that the considered two populations will approach spatially homogeneous distributions in the large time limit, provided that either the total population number of foragers or that of exploiters is appropriately small.