菲茨休 - 南云方程

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菲茨休 - 南云方程 Maple 3d 图
菲茨休 - 南云方程 Maple 动画
菲茨休 - 南云方程 Maple 图

菲茨休 - 南云方程(Fitzhugh-Nagumo equation)是一个非线性偏微分方程,由Richard FitzHugh南雲仁一提出,描述了在高于阈值的常电流刺激下神经元动作电位的周期性振荡[1]

\frac{\partial u}{\partial t}=D*\frac{\partial^2 u}{\partial^2 x^2}-u*(1-u)*(a-u)

利用Maple软件包TWSolution可得行波解[2]


u(x,t)= {1/2-(1/2)*\tanh((1/4)*\frac{\sqrt{2*x}}{\sqrt(d)}+(1/4)*t)}

u(x, t) = 1/2+(1/2)*tanh(_C1+(1/4)*sqrt(2)*x-(1/4)*t)

u(x, t) = 1/2+(1/2)*tanh(_C1-(1/4)*sqrt(2)*x-(1/4)*t)

1/2-(1/2)*tanh(_C1-(1/4)*sqrt(2)*x+(1/4)*t)

u(x, t) = 1/2-(1/2)*tanh(_C1+(1/4)*sqrt(2)*x+(1/4)*t)

File:1-Fitzhugh Nagumo plot 4.jpg 
File:1-Fitzhugh Nagumo plot 6.jpg 
File:1-Fitzhugh Nagumo plot 8.jpg 
File:1-Fitzhugh Nagumo plot 11.jpg 
 

参考文献[编辑]

  1. ^ Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential Equations p147-172 Academy Press
  2. ^ Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential Equations p436 Academy Press
  1. *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社
  2. *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
  3. 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
  4. 王东明著 《消去法及其应用》 科学出版社 2002
  5. *何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445
  6. Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
  7. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
  8. Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
  9. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
  10. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
  11. Dongming Wang, Elimination Practice,Imperial College Press 2004
  12. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
  13. George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759

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