Summary
In this work, we initiate a stability study of multispecies communities in stochastic environment by-using Itô's differential equations as community models. By applying the decomposition-aggregation approach in the context of Liapunov's direct method, we will obtain sufficient condition for stability in the mean of the equilibrium populations. As a by-product of this analysis, we will exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear and time-varying perturbations.
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The research reported herein was supported by NASA Grant NGR 05-017-010.
During the Summer of 1974, Professor G. S. Ladde was a Visiting Researcher on the NASA Grant NGR 05-017-010 at the School of Engineering, University of Santa Clara. Santa Clara, CA 95053, U.S.A.
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Ladde, G.S., Šiljak, D.D. Stability of multispecies communities in randomly varying environment. J. Math. Biology 2, 165–178 (1975). https://doi.org/10.1007/BF00275926
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DOI: https://doi.org/10.1007/BF00275926