Nonlinear identification of neuron models

The paper discusses when and how a nonlinear autonomous system can be uniquely identified from periodic data. This is a central problem in systems biology, where it e.g. arises when the dynamics of spiking neurons are modeled. The paper illustrates the problem by least squares identification of two autonomous neuron models, of order 4 and 2. The Hodgkin-Huxley model is well established, however it is of fourth order. As previously proved, this may not allow a unique identification from spiking neuron data. The paper illustrates this conclusion numerically, by least squares identification of a second order polynomial autonomous model, using spiking data generated by a fourth order Hodgkin-Huxley model. Further support is provided by identification of the second order FitzHugh-Nagumo model which can be exactly described by the model structure of the applied least squares algorithm. The Fitz-Hugh-Nagumo model can hence be uniquely identified from spiking neuron data. The paper also discusses computational complexity and provides results on the noise sensitivity of the applied least squares algorithm, when the sampling period is varied.