https://doi.org/10.1140/epjb/e2004-00399-x
Stability analysis of fronts in a tristable reaction-diffusion system
Institut für Theoretische Physik, Otto-von-Guericke-Universität,
Universitätsplatz 2, 39106 Magdeburg, Germany
Corresponding author: a kassner@physik.uni-magdeburg.de
Received:
4
November
2003
Revised:
9
August
2004
Published online:
23
December
2004
A stability analysis is performed analytically for the
tristable reaction-diffusion equation, in which a quintic reaction term
is approximated by a piecewise linear function. We obtain growth rate
equations for two basic types of propagating fronts, monotonous and
nonmonotonous ones. Their solutions show that the monotonous front is
stable whereas the nonmonotonous one is unstable. It is found that
there are two values of the growth rate for the most dangerous modes
(corresponding to the longest possible wavelengths), 
and
, for the monotonous front, so that at the
perturbation eigenfunction is positive whereas when it
changes sign. It is also noted that the eigenvalue becomes
negative in an inhomogeneous system with a particular (stabilizing)
inhomogeneity. Counting arguments for the number of eigenmodes of the
linear stability operator are presented.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 47.20.Ma – Interfacial instability / 47.54.+r – Pattern selection; pattern formation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
