The deterministic state of a model corresponds to steady-state values $$\overline{m}$$ of the exogenous process. States and controls satisfy:
$$\overline{s} = g\left(\overline{m}, \overline{s}, \overline{x}, \overline{m} \right)$$
$$0 = \left[ f\left(\overline{m}, \overline{s}, \overline{x}, \overline{m}, \overline{s}, \overline{x} \right) \right]$$
where $$g$$ is the state transition function, and $$f$$ is the arbitrage equation. Note that the shocks, $$\epsilon$$, are held at their deterministic mean.
The steady state function consists in solving the system of arbitrage equations for the steady state values of the controls, $$\overline{x}$$, which can then be used along with the transition function to find the steady state values of the state variables, $$\overline{s}$$.
dolo.algos.steady_state.residuals(model: dolo.compiler.model.Model, calib=None) → Dict[str, List[float]]