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Bifurcation Phenomena from Standing Pulse Solutions in Some Reaction-Diffusion Systems

Authors:	Hideo Ikeda Tsutomu Ikeda

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. (>0) is a sufficiently small parameter and is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when 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 is discussed for the piecewise linear nonlinearities f and g.

Keywords:	singular perturbation standing pulses stability Hopf bifurcation reaction-diffusion system
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