Using the "dynamical parameter estimation" (DPE) formulation of parameter and state estimation in models of nonlinear systems, we study the estimation of all parameters in two neuron models, including the four-dimensional standard Hodgkin-Huxley model and the two-dimensional Morris-Lecar model. DPE couples data from an observed system to synchronize the model and the data in a balanced manner. Parameters, unobserved states, and coupling/control variables are determined by the minimization of a synchronization cost function subject to the model equations of motion. In the implementation of DPE, we use the "direct method" for the numerical solution of the equivalent optimal tracking problem, employing the numerical optimization package SNOPT. We find that the numerical procedure for searching in parameter and state space performs in an accurate manner when the system is significantly perturbed from its attractor by external forcing. By driving the neuron of its attractor, it is forced to explore, in a transient manner, the phase space of the system, thus distinguishing distinct models with similar attractors.
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