Abstract
A formalism to describe the interactive growth of two or more organisms in a given environment is presented. This is a vector generalization of the scheme developed by Castorina et al. [1] to classify and interpret non-linear ontogenetic growth formulas, which can be applied to such complex self-organizing systems as solid tumors. A theorem that leads to the explicit solutions of the resulting equations is proven. These solutions can describe synergetic, antagonistic, and cooperative growth, and can be applied to both biological and ecological problems.
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