In this paper, we investigate the global behavior of a predator–prey chemotaxis model with loop \(\begin{aligned} \begin{aligned} {\left\{ \begin{array}{ll} u_t=d_1\Delta u+\chi _{11}\nabla \cdot (u\nabla w)+\chi _{12}\nabla \cdot (u\nabla z)+\mu _1 u(1-u-e_1 v), & x \in \Omega , \, t> 0,\\ v_t=d_2\Delta v-\chi _{21}\nabla \cdot (v\nabla w)-\chi _{22}\nabla \cdot (v\nabla z) +\mu _2 v(1+e_2 u-v), & x \in \Omega , \, t> 0,\\ w_t=d_3\Delta w-\beta _1 w+\alpha _{11}u+\alpha _{12}v, & x \in \Omega , \, t> 0,\\ z_t=d_4\Delta z-\beta _2 z+\alpha _{21}u+\alpha _{22}v, & x \in \Omega , \, t > 0. \end{array}\right. } \end{aligned} \end{aligned}\) under the homogeneous Neumann boundary conditions in a bounded smooth domain \(\Omega \subset \mathbb {R}^n\) \((n\ge 1)\) with smooth boundary \(\partial \Omega \) . Here, the parameters \(d_1\) , \(d_2\) , \(d_3\) , \(d_4\) , \(\chi _{ij}\) , \(\alpha _{ij}\) , \(\mu _i\) , \(e_i\) , \(\beta _i\) , (i, \(j=1\) ,2) are positive constants. We prove that for spatial dimension \(n \le 2\) and any sufficiently regular initial data, the model admits a unique, globally bounded classical solution without requiring any restrictions on the parameters. Furthermore, by constructing appropriate Lyapunov functionals, we establish the following convergence results: (i) If \(e_{1} < 1\) and \(\frac{\mu _{i}}{\chi _{ij}^{2}}\) is sufficiently large, the global solution (u, v, w, z) converges exponentially to the positive equilibrium. (ii) If \(e_{1}\ge 1\) and both \(\frac{\mu _{2}}{\chi _{21}^{2}}\) and \(\frac{\mu _{2}}{\chi _{22}^{2}}\) are sufficiently large, the global solution converges to the semi-trivial equilibrium with exponential decay when \(e_{1} > 1\) , and with algebraic decay when \(e_{1} = 1\) .
