This is a bit outside our normal area of expertise, but it looks interesting.
Thyroid hormones play an important role in metabolism, growth and differentiation. Therefore, exact regulation of thyroid hormone levels is vital for most organisms. The mechanism for the feedback control known, but the dynamics are still a bit of a mystery. There’s an interesting page on the different models for thyrotropic feedback control at the Midizinische Kybernetic (Medical Cybernetics) site. SimThyr is an open source Pascal-based simulation program for the pituitary thyroid feedback control mechanism that explores these models and makes predictions for dynamics based on parameters of the feedback mechanism.