Boundedness in a high-dimensional forager-exploiter model with nonlinear resource consumption by two species

We investigate a forager-exploiter model in a high-dimensional smooth bounded domain with zero-flux Neumann boundary condition:... ut =.u -.1. . (u. w), x. O, t> 0, vt =.v -.2. . (v. u), x. O, t> 0, wt = d.w - u+v (1+u+v). w - mu w + r(x, t), x. O, t> 0. This model characterizes the social interactions between the two species, foragers and exploiters, denoted by u and v, searching for the same food resource w. The positive taxis effects.1 and.2 reflect doubly tactic modelling hypothesis that the foragers chase food resource directly, while the exploiters follow after them. The spatio-temporal dynamics of food resource include its reaction-diffusion at rate d, natural reduction at rate mu, renewed production at rate r and especially its nonlinear consumption by the two species. For a positive constant. weighing the nonlinear sensitivity of resource consumption rate, we find a sufficient condition such that the system possesses a unique nonnegative global bounded classical solution.