Dynamics in two-predator and one-prey models with signal-dependent motility

This paper deals with the global boundedness and asymptotic stability of the solution of the two-predator and one-prey systems with density-dependent motion in a n-dimensional bounded domain with Neumann boundary conditions. In a previous paper, Qiu et al. (J Dyn Differ Equ, 1-25, 2021) proved the global existence and uniform boundedness of classical solution by limiting the conditions on motility functions and the coefficients of logistic source. By contrast, we relax the limitation conditions in Qiu et al. (2021) by constructing the weight function. Moreover, under diverse competition circumstances, the global stabilities of nonnegative spatially homogeneous equilibria for the special model are established.

Automated summary

This paper investigates the global boundedness and asymptotic stability of the solution of the two-predator and one-prey systems with density-dependent motion in a n-dimensional bounded domain with Neumann boundary conditions. The previous paper by Qiu et al. (J Dyn Differ Equ, 1-25, 2021) proved the global existence and uniform boundedness of classical solution by limiting the conditions on motility functions and the coefficients of logistic source. In contrast, this paper relaxes the limitation conditions in Qiu et al. (2021) by constructing the weight function. Moreover, the global stabilities of nonnegative spatially homogeneous equilibria for the special model are established.