State and parameter estimation for canonic models of neural oscillators.
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.
Tyukin
Ivan
I
Department of Mathematics, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom. I.Tyukin@le.ac.uk
Steur
Erik
E
Nijmeijer
Henk
H
Fairhurst
David
D
Song
Inseon
I
Semyanov
Alexey
A
Van Leeuwen
Cees
C
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