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We suggest a novel approach to treating symbiotic relations betweenbiological species or social entities. The main idea is the characterisation ofsymbiotic relations of coexisting species through their mutual influence ontheir respective carrying capacities, taking into account that this influencecan be quite strong and requires a nonlinear functional framework. Wedistinguish three variants of mutual influence, representing the main types ofrelations between species: (i) passive symbiosis, when the mutual carryingcapacities are influenced by other species without their direct interactions;(ii) active symbiosis, when the carrying capacities are transformed byinteracting species; and (iii) mixed symbiosis, when the carrying capacity ofone species is influenced by direct interactions, while that of the otherspecies is not. The approach allows us to describe all kinds of symbiosis,mutualism, commensalism, and parasitism within a unified scheme. The case oftwo symbiotic species is analysed in detail, demonstrating several dynamicalregimes of coexistence, unbounded growth of both populations, growth of one andelimination of the other population, convergence to evolutionary stable states,and everlasting population oscillations. The change of the dynamical regimesoccurs by varying the system parameters characterising the destruction orcreation of the mutual carrying capacities. The regime changes are associatedwith several dynamical system bifurcations.

New Approach to Modeling Symbiosis in Biological and Social Systems