Stability and Instability of Improved Heimburg-Jackson Model to Nerve Pulse Propagation

Authors

  • Nikolai Kutev* Institute of Mathematics and Informatics, BAS
  • Natalia Kolkovska
  • Milena Dimova

DOI:

https://doi.org/10.11145/457

Abstract

There are a number of mathematical models to В nerve pulse propagation in biomembranes, as Hodgkin--Huxley, FitzHugh--Nagumo and Heimburg--Jackson models, see, e.g., [1,2]. However, these models do not describe В adequately all observed phenomena.Recently in [2], generalized Boussinesq equation with quadratic--cubic nonlinearity is proposed В as an improvement of the well-known Heimburg--Jackson model.In this study we prove В analytically В the orbital stability and instability of solitary waves to the improved Heimburg--Jackson model (1). The results depend on the relationship betweenВ  all parameters of the model.В For the set of data, obtained experimentally, our theoretical results are in full agreement with the numerical simulations, presented in [3].References:[1] T. Heimburg, A.D. Jackson, On soliton proprgation in biomembranes and nerves, Proc. Natl. Acad. Sci. USA 102 9790--9795, 2005.[2] J. Engelbrecht, K. Tamm, T. Peets, On mathematical modelling of solitary pulses in cylindrical biomembranes, Biomech Model Mechanobiol. 14 159--167, 2015.[3] B. Lautrup, R. Appali, A.D. Jackson, T. Heimburg, The stability of solitonsin biomembranes and nerves, Eur. Phys. J. E В 34 1--9, 2011.

Author Biographies

Nikolai Kutev*, Institute of Mathematics and Informatics, BAS

Natalia Kolkovska

Milena Dimova

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Published

2015-04-23

Issue

Vol. 2 No. 1 (2015)

Section

Conference Contributions

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