Spatial correlations in the decay from an unstable state in the Malthus Verhulst model

The transient behavior during the decay of an initial unstable state of a reaction diffusion model describing the inhomogeneous fluctuations in the Malthus Verhulst problem applicable to the slowly varying part of the electrical field in a laser cavity was studied. The analysis is performed in a region of the control parameters space where a systematic approximation scheme can be introduced. The enhancement of fluctuations during the transient leads to the growth of the correlation length above its steady state value.