Problem with the perturbation method applying to the nonlinear system.

Question

There is a system of equations with initial conditions: $$ \begin{cases} \dot x = y + a \cdot x \cdot y, \quad x(0) = 1, \\ \dot y = - x - b\cdot x \cdot y, \quad y(0) = 0;\end{cases} $$ where $a$ and $b$ are small parameters with the same order. I have to apply perturbation approach to this system, and to find the solution in the second order of $a$ and $b$. My problem: small corrections of different orders can be in resonance, and the small corrections will not be small when $a$ and $b$ go to $0$. I have to demand the absence of resonances, and to satisfy this requiring by frequency corrections. First, I will show what I do:$$$$The zeroth order:$$x(t)\approx x_{0}(t)\\y(t) \approx y_{0}(t)\\ \begin{cases} \dot x_{0}(t)=y_{0}(t),\quad x_{0}(0)=1,\\ \dot y_{0}(t)=-x_{0}(t), \quad y_{0}(0)=0; \end{cases} $$ The first order: $$x(t)\approx x_{0}(\omega t)+x_{1}(t)\\y( t) \approx y_{0}(\omega t) + y_{1}(t)\\ \omega = 1 + \omega_{1}\\ \begin{cases} \dot x_{1}(t)=y_{1}(t) + a \cdot x_{0}(\omega t) \cdot y_{0} (\omega t) - \omega_{1} \cdot x_{0}'(\omega t),\quad x_{1}(0)=0,\\ \dot y_{1}(t)=-x_{1}(t)-b \cdot x_{0}(\omega t) \cdot y_{0}(\omega t)-\omega_{1} \cdot y_{0}'(\omega t), \quad y_{1}(0)=0; \end{cases}\\Resonance \quad abscence \quad condition: \omega_{1}=0 $$ The second order:$$x(t) \approx x_{0}(\omega t) + x_{1}(\omega t) + x_{2}(t) \\ y(t) \approx y_{0}(\omega t) + y_{1}(\omega t) + y_{2}(t) \\ \omega = 1 + \omega_{1} + \omega_{2} = 1 + \omega_{2} \\ \begin{cases} \dot x_{2}(t) = y_{2}(t) + a \cdot (x_{0}(\omega t) \cdot y_{1} (\omega t) + x_{1}(\omega t) \cdot y_{1}(\omega t))-\omega_{2} \cdot x_{0}'(\omega t), \quad x_{2}(0)=0, \\ \dot y_{2}(t) = -x_{2}(t) - b \cdot (x_{0}(\omega t) \cdot y_{1} (\omega t) + x_{1}(\omega t) \cdot y_{1}(\omega t))-\omega_{2} \cdot y_{0}'(\omega t), \quad y_{2}(0)=0; \end{cases} \\ Resonance \quad abscence \quad condition: \quad ? \\ $$ For each order I have a system of equations with eigen frequence $= 1$. So, $\omega_{2}$ is not enaugh to satisfy resonance absence. The question is: how can I avoid the resonances?