Modeling Symbiosis by Interactions Through Species Carrying Capacities

Physica D: Nonlinear Phenomena, Vol. 241, pp. 1270-1289, 2012

52 Pages Posted: 8 Jun 2012

See all articles by Vyacheslav I. Yukalov

Vyacheslav I. Yukalov

Joint Institute for Nuclear Research; D-MTEC, ETH Zurich

E.P. Yukalova

Joint Institute for Nuclear Research

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Tokyo Institute of Technology

Date Written: June 7, 2012

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.

Suggested Citation

Yukalov, Vyacheslav I. and Yukalova, E.P. and Sornette, Didier, Modeling Symbiosis by Interactions Through Species Carrying Capacities (June 7, 2012). Physica D: Nonlinear Phenomena, Vol. 241, pp. 1270-1289, 2012, Available at SSRN: https://ssrn.com/abstract=2079438

Vyacheslav I. Yukalov (Contact Author)

Joint Institute for Nuclear Research ( email )

Bogolubov Laboratory of Theoretical Physics
Dubna, 141980
Russia

D-MTEC, ETH Zurich ( email )

Zurich
Switzerland

E.P. Yukalova

Joint Institute for Nuclear Research ( email )

Joliot-Curie 6
Dubna, 141980
Russia

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Tokyo Institute of Technology ( email )

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

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