Simple and sufficient conditions for generalized Lotka-Volterra models to be globally stable in the positive orthant are described. Similar conditions for global stability in general nonlinear population models are also given. These conditions imply that if each species in a complex ecosystem sustains density-dependent mortalities due to intraspecific interactions and the interspecific interactions are not too strong then the ecosystem is globally stable.
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B. S. Goh (1977) studied this question.
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