Abstract
A rigorous asymptotic spiral solution to an excitable reaction diffusion system is found by separating space into two scaling regions: an "outer region", having the same spatial scaling as the overall spiral structure, which exhibits a singularity at the spiral tip; and a "core" region around the spiral tip, where space is scaled so as to resolve the tip singularity. The stability of the spiral structure is investigated for both the outer region, which is found to possess no intrinsic instability, and the core region which is found to be unstable. Both the zero and small diffusion systems are found to exhibit qualitatively similar behaviour. The implication of these results for both experiment and simulation, in particular within the context of the observed "meandering" instability, are addressed.
| Original language | English |
|---|---|
| Pages (from-to) | 115-139 |
| Number of pages | 25 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 70 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 1 Jan 1994 |
| Externally published | Yes |
Bibliographical note
Funding Information:We would like to acknowledgteh e invaluable assistanceo f Dwight Barkley, as well as useful discussionws ith A. Karma and A. Winfree. The work of D.A.K. was supportedb y US Dept. of Energy Grant DE-FG-02-85ER54189th, e work of H.L. and W.R. was supportedin part by National ScienceF oundationG rant no. DMR-9115413.
Funding
We would like to acknowledgteh e invaluable assistanceo f Dwight Barkley, as well as useful discussionws ith A. Karma and A. Winfree. The work of D.A.K. was supportedb y US Dept. of Energy Grant DE-FG-02-85ER54189th, e work of H.L. and W.R. was supportedin part by National ScienceF oundationG rant no. DMR-9115413.
| Funders | Funder number |
|---|---|
| National ScienceF oundationG | |
| US Dept. of Energy | DE-FG-02-85ER54189th |