Superlinear indefinite systems: Beyond Lotka–Volterra models

This paper analyzes the dynamics of a superlinear indefinite parabolic system. As a byproduct, a number of new results related to population dynamics and economy are obtained. Among them, it is shown that the presence of refuge areas in competitive environments is an optimal mechanism to avoid extinction, and that incorporating local symbiosis in competitive environments increases productivity and allows avoiding extinction of the ‘weaker’ species. Undoubtedly, a paradigm of global markets and possibly of Earth biodiversity. Our analysis combines a series of well-known results for systems with some very recent pioneering findings within the context of superlinear indefinite equations.