title: State and parameter estimation for canonic models of neural oscillators.
abstract: We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent diffeomorphism exists, such that the original model equations can be transformed into adaptive canonic observer form. For a large class of model neurons, however, state and parameter reconstruction is possible nevertheless. We propose a method which, subject to mild conditions on the richness of the measured signal, allows model parameters and state variables to be reconstructed up to an equivalence class.
authors.affiliation: Department of Mathematics, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom. I.Tyukin@le.ac.uk
authors.forename: Ivan
authors.initials: I
authors.lastname: Tyukin
authors.forename: Erik
authors.initials: E
authors.lastname: Steur
authors.forename: Henk
authors.initials: H
authors.lastname: Nijmeijer
authors.forename: David
authors.initials: D
authors.lastname: Fairhurst
authors.forename: Inseon
authors.initials: I
authors.lastname: Song
authors.forename: Alexey
authors.initials: A
authors.lastname: Semyanov
authors.forename: Cees
authors.initials: C
authors.lastname: Van Leeuwen
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted