TRANSVERSE INSTABILITY OF SPIKE AUTOSOLITONS

We study transverse instability of one of the basic types of localized patterns - spike autosolitons - arising in different reaction-diffusi on systems. We show that in contrast to domain patterns forming in Fit zHugh-Nagumo type systems the spike autosolitons in the form of stripe s (strata) are always unstable to shortwave transverse perturbations. We analyze the growth rates of these perturbations and find conditions for the static spike autosoliton to transform into a traveling one or more complex spike patterns which were recently observed in experimen ts and simulations.