Critical mass curves for a short-ranged chemical signaling loop

In this paper, we consider a two-species and two-stimuli chemotaxis system, in which the interactions of the two species form a short-ranged chemical signaling loop. By substantially improving the known bounded conditions and blow-up conditions obtained in Lin and Xiang (J Nonlinear Sci 29:551–591, 2019), we establish the critical mass curves for radial solutions of the system to distinguish the global boundedness and finite-time blow-up perfectly. Moreover, we extend our results to the nonradial solutions of the system partially.