Article ID Journal Published Year Pages File Type
1898560 Physica D: Nonlinear Phenomena 2012 20 Pages PDF
Abstract

We introduce a mathematical model of symbiosis between different species 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.

► A model of symbiosis is advanced. ► Species interactions are realized through species carrying capacities. ► Classification of symbiosis types is given.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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