Global dynamics and spatiotemporal patterns of a two‐species chemotaxis system with chemical signaling loop and Lotka–Volterra competition

Abstract This paper considers a two‐species chemotaxis system with chemical signaling loop and Lotka–Volterra competition kinetics under the homogeneous Newman boundary condition in smooth bounded domains. The global existence and boundedness of solutions for the parabolic–elliptic/parabolic–parabolic system are established. In the strong competition case, the global stability of the semitrivial constant steady state is obtained under certain parameter conditions. Linear analyzes and numerical simulations demonstrate that chemical signaling loop can significantly impact population dynamics, and admit the coexistence in the exclusion competitive case, including nonconstant steady states, chaos, and spatially inhomogeneous time‐periodic types.