total dynamical system can describe the meson spectra very well and the results are in agreement with experimental data [@Li:2013oda].

However, it is not an easy task to solve the full system at finite temperature and chemical potential. Therefore, in this work, we use the quenched dynamical model with the flavor background added on the dilaton background as a probe. The chiral and deconfinement phase transitions at finite temperature in the quenched dynamical holographic QCD model has been investigated in Ref. [@Fang:2015ytf]. Here, we extend this scenario to finite chemical potential case, and try to study chiral and deconfinement phase transition in the $T - \mu$ plane.

To extend the quenched dynamical holographic QCD model in Refs. [@Li:2012ay; @Li:2013oda; @Li:2014dsa] to finite chemical potential , we introduce an extra $U(1)$ field in the Einstein-Dilaton-Maxwell framework, and the action in the string frame takes the form of: $$\begin{aligned}
 S_{total}^s&&=S_G^s+S_M^s,\\
S_G^s &&= \frac{1}{16\pi G_5}\int d^5x\sqrt{-g^s}e^{-2\Phi}[R^s+4\partial_\mu\Phi\partial^\mu\Phi-V_G^s(\Phi)-\frac{h(\Phi)}{4}e^\frac{4\Phi}{3} F_{\mu\nu}F^{\mu\nu}]\label{sb},\\
S_M^s &&= -\int d^5x\sqrt{-g^s}e^{-\Phi}Tr[\nabla_\mu X^{\dagger}\nabla^\mu X+V_X^s(|X|,F_{\mu\nu}F^{\mu\nu} )]. \label{SMatter}\end{aligned}$$ Here $S_{total}$ is the full 5D action, $S_G$ is the 5D action for dilaton background describing gluodynamics, and $S_M$ is the 5D action for matter sector describing chiral dynamics, respectively. The lower-case $s$ represents the string frame, $g^s$ 