Stability in higher-derivative matter fields theories

We discuss possible instabilities in higher-derivative matter fields theories. These theories has two free parameters ${\beta }_1$ and ${\beta }_4$. By using dynamical system approach we explicitly demonstrate that for stability of Minkowski space in expanding Universe it is need condition ${\beta }_4<0$. By using quantum field theory approach we also find additional restriction for parameters ${\beta }_1>-\frac{1}{3}{\beta }_4$ which is need to avoid tachyon-like instability.