Particle filtering based identification for autonomous nonlinear ODE models

This paper presents a new black-box algorithm for identification of a nonlinear autonomous system in stable periodic motion. The particle filtering based algorithm models the signal as the output of a continuous-time second order ordinary differential equation (ODE). The model is selected based on previous work which proves that a second order ODE is sufficient to model a wide class of nonlinear systems with periodic modes of motion, also systems that are described by higher order ODEs. Such systems are common in systems biology. The proposed algorithm is applied to data from the well-known Hodgkin-Huxley neuron model. This is a challenging problem since the Hodgkin-Huxley model is a fourth order model, but has a mode of oscillation in a second order subspace. The numerical experiments show that the proposed algorithm does indeed solve the problem.