Back
Full-text
Journal article

New Approach to Modeling Symbiosis in Biological and Social Systems

  • Yukalov, V. I. Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
  • Yukalova, E. P. Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980, Russia
  • Sornette, D. Swiss Finance Institute, c/o University of Geneva, 40 Blvd. Du Pont d'Arve, CH 1211 Geneva 4, Switzerland
  • 2014-10-3
Published in:
  • International Journal of Bifurcation and Chaos. - World Scientific Pub Co Pte Lt. - 2014, vol. 24, no. 09, p. 1450117
English We suggest a novel approach to treating symbiotic relations between biological species or social entities. The main idea is the characterization of symbiotic relations of coexisting species through their mutual influence on their respective carrying capacities, taking into account that this influence can be quite strong and requires a nonlinear functional framework. We distinguish three variants of mutual influence, representing the main types of relations between species: (i) passive symbiosis, when the mutual carrying capacities are influenced by other species without their direct interactions; (ii) active symbiosis, when the carrying capacities are transformed by interacting species; and (iii) mixed symbiosis, when the carrying capacity of one species is influenced by direct interactions, while that of the other species is not. The approach allows us to describe all kinds of symbiosis, mutualism, commensalism, and parasitism within a unified scheme. The case of two symbiotic species is analyzed in detail, demonstrating several dynamical regimes of coexistence, unbounded growth of both populations, growth of one and elimination of the other population, convergence to evolutionary stable states, and everlasting population oscillations. The change of the dynamical regimes occurs by varying the system parameters characterizing the destruction or creation of the mutual carrying capacities. The regime changes are associated with several dynamical system bifurcations.
Language
  • English
Open access status
green
Identifiers
Persistent URL
https://sonar.ch/global/documents/283703
Statistics
Document views: 19 File downloads:
  • Full-text: 0