ISSN:
1432-1416
Keywords:
Oscillation
;
Excitability
;
Waves
;
Pulse waves
;
Rings
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract A simple one variable caricature for oscillating and excitable reaction-diffusion systems is introduced. It is shown that as a parameter, λ, varies the system dynamics change from oscillatory (λ 〉 λ 0) to excitable (λ 〈 λ 0) and the frequency of the oscillation vanishes as $$\sqrt {(\lambda - \lambda _0 )}$$ for λ ↘ λ0. When such dynamics are coupled by continuous diffusion in a ring geometry (1-space dimension), propagating wave trains may be found. On an infinite ring excitable devices lead to unique solitary waves which are analogous to “pulse” waves. A solvable example is presented, illustrating properties of dispersion, excitability, and waves. Finally it is shown that the caricature arises in a natural way from more general excitable/oscillatory systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00276897
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