ISSN:
1572-9222
Keywords:
singular perturbation
;
standing pulses
;
stability
;
Hopf bifurcation
;
reaction-diffusion system
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009098719440
