### Abstract

Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.

Original language | English (US) |
---|---|

Pages (from-to) | 1111-1137 |

Number of pages | 27 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 42 |

Issue number | 5 |

State | Published - Oct 1982 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*42*(5), 1111-1137.

**PROPAGATION PHENOMENA IN A BISTABLE REACTION-DIFFUSION SYSTEM.** / Rinzel, John; Terman, David.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 42, no. 5, pp. 1111-1137.

}

TY - JOUR

T1 - PROPAGATION PHENOMENA IN A BISTABLE REACTION-DIFFUSION SYSTEM.

AU - Rinzel, John

AU - Terman, David

PY - 1982/10

Y1 - 1982/10

N2 - Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.

AB - Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented.

UR - http://www.scopus.com/inward/record.url?scp=0020191444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020191444&partnerID=8YFLogxK

M3 - Article

VL - 42

SP - 1111

EP - 1137

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -