Nonlinear Dynamics

, Volume 85, Issue 4, pp 2521–2533 | Cite as

A method for estimation of parameters in a neural model with noisy measurements

  • Ranjit Kumar UpadhyayEmail author
  • Argha Mondal
  • Chinmoy Paul
Original Paper


In this article, we establish a method for the estimation of parameters of a three-dimensional Hindmarsh–Rose (HR) neural model under noisy environment. It has been assumed that all the parameters are unknown and are expressed as the time-varying sinusoidal functions for the membrane voltage recordings. We apply the method to present the stochastic nature of parameters, applied current and membrane voltage. The proposed method shows that the estimation procedure needs a large number of time scales for which the solution will be more accurate and it provides the relation between the parameters. The stochastic 3D HR model is used, and the mean and variances are calculated. Our analysis explains how the parameters are estimated and it helps us to select an optimal simulation procedure. The estimation procedure is also derived for a particular case when the parameters are constants instead of time-varying functions. This paper reports the application of estimation technique to experimental studies in neural computation.


Stochastic Hindmarsh–Rose neural system Time-varying parameters White noise Estimation technique 



The first author would like to thank the Issac Newton Institute for Mathematical Sciences for its hospitality during the programme [Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation] supported by EPSRC Grant Number EP/K032208/1.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Ranjit Kumar Upadhyay
    • 1
    • 2
    Email author
  • Argha Mondal
    • 2
  • Chinmoy Paul
    • 2
  1. 1.Isaac Newton Institute for Mathematical SciencesCambridgeUK
  2. 2.Department of Applied MathematicsIndian School of MinesDhanbadIndia

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