Abstract
We study the existence and uniqueness of traveling wave solutions of the discrete buffered bistable equation. Buffered excitable systems are used to model, among other things, the propagation of waves of increased calcium concentration, and discrete models are often used to describe the propagation of such waves across multiple cells. We derive necessary conditions for the existence of waves, and, under some restrictive technical assumptions, we derive sufficient conditions. When the wave exists it is unique and stable.
Original language | English |
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Pages (from-to) | 605-652 |
Number of pages | 48 |
Journal | Journal of Mathematical Biology |
Volume | 55 |
Issue number | 5-6 |
DOIs | |
Publication status | Published - 2007 Nov |
Externally published | Yes |
Keywords
- Bistable
- Buffer
- Calcium
- Traveling wave
ASJC Scopus subject areas
- Modelling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics