CATASTROPHIC EXTINCTION, NOISE-STABILIZED TURBULENCE AND UNPREDICTABILITY OF COMPETITION IN A MODIFIED VOLTERRA-LOTKA MODEL

Spatial coexistence and competition among species is investigated thro ugh a modified Volterra-Lotka model which takes into account sexual br eeding. This allows the population specific growth rate to depend on t he population density. As a result of this modification the degeneracy inherent in the classical model is eliminated and qualitatively novel regimes are observed, as demonstrated by parametric analysis of the m odel. In the case where the corresponding parameters of competing spec ies do not differ significantly the model can be reduced to a single G inzburg-Landau type equation. The spatially distributed model is analy zed both in the absence and in the presence of noise mimicking inheren t fluctuations in birth and death rates. It is shown that noise can qu alitatively change the behavior of the system. Not only does it induce the formation of spatial patterns, but also switches on endless turbu lent-like rearrangement of the system. When initially unpopulated habi tat is occupied by competing species even a very low-intensity noise m akes the final state of the system totally unpredictable and sensitive to any fluctuations. (C) 1996 American Institute of Physics.