Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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RELATIVISTIC INTERPLAY BETWEEN ADAPTIVE MOVEMENT AND MOBILITY ON BIODIVERSITY IN THE ROCK-PAPER-SCISSORS GAME

  • PARK, JUNPYO (DEPARTMENT OF MATHEMATICAL SCIENCES, ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY) ;
  • JANG, BONGSOO (DEPARTMENT OF MATHEMATICAL SCIENCES, ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY)
  • Received : 2020.11.17
  • Accepted : 2020.12.07
  • Published : 2020.12.25
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Abstract

Adaptive behaviors are one of ubiquitous features in evolutionary dynamics of populations, and certain adaptive behaviors can be witnessed by individuals' movements which are generally affected by local environments. In this paper, by revisiting the previous work, we investigate the sensitivity of species coexistence in the system of cyclic competition where species movement can be affected by local environments. By measuring the extinction probability through Monte-Carlo simulations, we find the relativistic effect of weights of local fitness and exchange rate for adaptive movement on species biodiversity which promotes species coexistence as the relativistic effect is intensified. In addition, by means of basins of initial conditions, we also found that adaptive movement can also affect species biodiversity with respect to the choice of initial conditions. The strong adaptive movement can eventually lead the coexistence as a globally stable state in the spatially extended system regardless of mobility.

Keywords

Acknowledgement

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2015S1A5A2A03049830)

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