Search Advanced

Mathematical Biosciences and Engineering

2007, Volume 4, Issue 1: 113-129. doi: 10.3934/mbe.2007.4.113
Previous Article Next Article

The stability of stationary fronts for a discrete nerve axon model

  • 1.
    High Bridge, NJ 08829
  • Received: 01 April 2006 Accepted: 29 June 2018 Published: 01 November 2006

  • MSC : 34K20,37K45.

  • We consider the stability of single-front stationary solutions to a spatially discrete reaction-diffusion equation which models front propagation in a nerve axon. The solution's stability depends on the coupling parameter, changing from stable to unstable and from unstable to stable at a countably infinite number of values of this diffusion coefficient.

    Citation: Christopher E. Elmer. The stability of stationary fronts for a discrete nerve axon model[J]. Mathematical Biosciences and Engineering, 2007, 4(1): 113-129. doi: 10.3934/mbe.2007.4.113

    Related Papers:

    [1] Daniel Špale, Petr Stehlík . Stationary patterns in bistable reaction-diffusion cellular automata. Mathematical Biosciences and Engineering, 2022, 19(6): 6072-6087. doi: 10.3934/mbe.2022283
    [2] Alan Dyson . Traveling wave solutions to a neural field model with oscillatory synaptic coupling types. Mathematical Biosciences and Engineering, 2019, 16(2): 727-758. doi: 10.3934/mbe.2019035
    [3] Yuanfei Li, Xuejiao Chen . Spatial decay bound and structural stability for the double-diffusion perturbation equations. Mathematical Biosciences and Engineering, 2023, 20(2): 2998-3022. doi: 10.3934/mbe.2023142
    [4] Ali Moussaoui, Vitaly Volpert . The influence of immune cells on the existence of virus quasi-species. Mathematical Biosciences and Engineering, 2023, 20(9): 15942-15961. doi: 10.3934/mbe.2023710
    [5] Marcin Choiński, Mariusz Bodzioch, Urszula Foryś . A non-standard discretized SIS model of epidemics. Mathematical Biosciences and Engineering, 2022, 19(1): 115-133. doi: 10.3934/mbe.2022006
    [6] Chichia Chiu, Jui-Ling Yu . An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems. Mathematical Biosciences and Engineering, 2007, 4(2): 187-203. doi: 10.3934/mbe.2007.4.187
    [7] Guangrui Li, Ming Mei, Yau Shu Wong . Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model. Mathematical Biosciences and Engineering, 2008, 5(1): 85-100. doi: 10.3934/mbe.2008.5.85
    [8] Swadesh Pal, Malay Banerjee, Vitaly Volpert . Spatio-temporal Bazykin’s model with space-time nonlocality. Mathematical Biosciences and Engineering, 2020, 17(5): 4801-4824. doi: 10.3934/mbe.2020262
    [9] Danfeng Pang, Yanni Xiao . The SIS model with diffusion of virus in the environment. Mathematical Biosciences and Engineering, 2019, 16(4): 2852-2874. doi: 10.3934/mbe.2019141
    [10] Lin Zhang, Yongbin Ge, Xiaojia Yang . High-accuracy positivity-preserving numerical method for Keller-Segel model. Mathematical Biosciences and Engineering, 2023, 20(5): 8601-8631. doi: 10.3934/mbe.2023378
  • We consider the stability of single-front stationary solutions to a spatially discrete reaction-diffusion equation which models front propagation in a nerve axon. The solution's stability depends on the coupling parameter, changing from stable to unstable and from unstable to stable at a countably infinite number of values of this diffusion coefficient.


  • This article has been cited by:

    1. Elizabeth Lydon, Brian E. Moore, Propagation failure of fronts in discrete inhomogeneous media with a sawtooth nonlinearity, 2016, 22, 1023-6198, 1930, 10.1080/10236198.2016.1255209
    2. Brian E. Moore, Joseph M. Segal, Stationary bistable pulses in discrete inhomogeneous media, 2014, 20, 1023-6198, 1, 10.1080/10236198.2013.800868
    3. A. R. Humphries, Brian E. Moore, Erik S. Van Vleck, Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion, 2011, 71, 0036-1399, 1374, 10.1137/100807156
  • Reader Comments
  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2410) PDF downloads(467) Cited by(3)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog