In this paper, we study the following three-species food chain chemotactic system with evasion effect \(\begin{aligned} {\left\{ \begin{array}{ll} u_{t}=d_1\Delta u+u(1-u)-b_1uv,& \quad x\in \Omega , t>0,\\ v_{t}=d_2\Delta v-\nabla \cdot \left( \xi v\nabla u\right) +\nabla \cdot \left( \chi _1v\nabla z\right) +uv-b_2vw-\theta _1v,& \quad x\in \Omega , t>0,\\ w_{t}=\Delta w-\nabla \cdot \left( \chi _2w\nabla v\right) +vw-\theta _2w^{\alpha }-w,& \quad x\in \Omega , t>0,\\ z_{t}=\Delta z+w^{\beta }-z,& \quad x\in \Omega , t>0, \end{array}\right. } \end{aligned}\) under homogeneous Neumann boundary conditions in a bounded domain \(\Omega \subset \mathbb {R}^2\) with smooth boundary, where the parameters \(d_1,d_2,b_1,b_2,\xi ,\chi _1,\chi _2,\theta _1,\theta _2,\alpha ,\beta \) are positive. By the suitable coupling energy estimates, we obtain that the system admits a unique globally bounded classical solution, provided that \(\alpha>4\beta ,\alpha >1\) . Additionally, we investigate an examination of the asymptotic stability of constant steady-state solution by constructing appropriate Lyapunov functionals and using the different parameter choices.
