Limit cycle models with perturbation techniques

For those interested in solving models featuring an attracting limit cycle with perturbation techniques:

I have developed the CSD perturbation toolbox which can also solve limit cycle models. The toolbox is completely based on the CoRRAM-M toolkit (2018 version) developed by Professor Alfred Maussner. To solve limit cycle models it uses code developed by Dana Galizia (see publication below).

The toolbox includes two examples which replicate the simulations of the limit cycle models in:

  • Beaudry, P., Galizia, D., & Portier, F. (2020). Putting the cycle back into business cycle analysis. American Economic Review, 110(1), 1-47.

  • Galizia, D. (2021). Saddle cycles: Solving rational expectations models featuring limit cycles (or chaos) using perturbation methods. Quantitative Economics, 12(3), 869-901.

The toolbox can only carry out two tasks:

  1. Solve a model (up to an order 3 approximation);
  2. Evaluate the policy function, taking the state variables as input.

This simple design of the CSD toolbox makes it useful for educational purposes, simulations, simple calibration exercises, and to obtain the initial guess for projection methods. The toolbox takes up less than 1 MB of disk space. One limitation is that it can currently only handle symbolic models.

I have attached the toolbox. It can also be found on or (573.0 KB)