Automated detection of chaotic and oscillatory regimes

Qualitative parameter estimation algorithms are a promising but underdeveloped class of inference methods [1]. They offer the ability to infer parameters when only qualitative features of the system are known or need to be specified. Here we adapt the unscented Kalman filter for identification of model parameters that give rise to a desired Lyapunov spectrum. This novel approach extends the reach of these techniques, allowing detection of the most complex and elusive dynamical behaviours. We demonstrate our method on three ODE models, including a simple model of the Hes1 regulatory system.