Modelling symbiosis in biological and social systems

Details Modelling symbiosis in biological and social systems Modelling symbiosis in biological and social systems

2010-03-10

arxiv.org/abs/1003.2092v1

Physics

Biological Physics

Latex file, 38 pages, 17 figures

Scientific paper

We introduce a general mathematical model of symbiosis between different entities by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies or to social, economic and financial societies. Our model includes three basic types: symbiosis with direct mutual interactions, symbiosis with asymmetric interactions, and symbiosis without direct interactions. In all cases, we provide a complete classification of all admissible dynamical regimes. The proposed model of symbiosis turned out to be very rich, as it exhibits four qualitatively different regimes: convergence to stationary states, unbounded exponential growth, finite-time singularity, and finite-time death or extinction of species.

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