Catastrophic extinction,noise-stabilized turbulence and unpredictability of competition in a modified Volterra-Lotka model

Spatial coexistence and competition among species is investigated through a modified Volterra-Lotka model which takes into account sexual breeding. This allows the population specific growth rate to depend on the 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 model. In the case where the corresponding parameters of competing species do not differ significantly the model can be reduced to a single Ginzburg-Landau type equation. The spatially distributed model is analyzed both in the absence and in the presence of noise mimicking inherent fluctuations in birth and death rates. It is shown that noise can qualitatively change the behavior of the system. Not only does it induce the formation of spatial patterns, but also switches on endless turbulent-like rearrangement of the system. When initially unpopulated habitat is occupied by competing species even a very low-intensity noise makes the final state of the system totally unpredictable and sensitive to any fluctuations. (c) 1996 American Institute of Physics.