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Kyung Hee Undergrad Student in Applied Mathematics Publishes in SCIE Journal as First Author

2024-01-05 Research

Research team led by Professor Junpyo Park at the Department of Applied Mathematics analyzes cyclic competition structures to illustrate causes of survival phase transitions

Student Ryoo Kyung Yang (Applied Mathematics, '19) has published in the top-ranked SCIE journal as the first author. Professor Junpyo Park congratulated the outstanding achievement made possible by the active participation of Student Yang in the core stages of research. The research findings were published in October 2023 in the international academic journal Chaos, Solitons and Fractals (IF=7.8) under the title, “Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity.”

The research team investigated through mathematical modeling how species biodiversity and survival probability change as the number of species in a multi-species cyclic competition system increases. The team diagrammatically identified the causes of common species survival phase transitions occurring with an increase in the number of species within the system.

While the evolutionary dynamics of cyclic competition system has been largely based on the underlying mechanism of rock-paper-scissors (RPS) involving three or five species, the complexity of actual ecosystems in nature poses limitations on mathematical models especially on the interaction structure in small-scale systems. Professor Park explained, “As the number of species increases, more diverse competition structures are formed within the system, so the number of species should be a key consideration for any complex system modeling.”

The research team analyzed the competition structure based on a seven-species model, which is a marked expansion over conventional model. Conducting simulations using traditional methodology, they observed the trend of interspecific biodiversity with variations in the diffusion factor. While some species among the seven exhibited similar phase transitions in biodiversity as in the conventional cyclic competition model, this phenomenon did not occur in all species. Utilizing graph structures, the research team analyzed why the transitions did not occur, with Student Yang playing a crucial role in this process. In her analysis, she discovered that the interspecific structure influences phase transitions in biodiversity.

The introduction of a lattice-based Monte Carlo simulation prediction model received commendation. Professor Park explained, “As the number of species increases, the simulation time also increases with more variables in the system. However, utilizing a lattice-based simulation can reduce simulation time and offer significant advantages in visualization."

The next goal of the research team is to develop mathematical guidelines for the evolutionary dynamics of large cyclic competition systems, extending beyond the scope of current research. Professor Park said, “We will incorporate data group analysis methods from the field of machine learning to better understand interspecific interaction structures and develop more effective interpretation methods.”

While research in evolutionary dynamics is actively pursued in the United States and Europe, the spectrum of research in Korea has been rather narrowly focused. Professor Park concluded, "Evolutionary dynamics is a field of research where various interdisciplinary approaches can intersect through mathematics as the common medium. Collaborative research between humanities and natural sciences, such as sociology, economics, physics, and chemistry, is very much a necessity in this area. To broaden the spectrum of evolutionary dynamics in the future, we plan to make efforts for the practical application of mathematics."

※ For further insights
- Explore Professor Park Junpyo's research profile
- Professor Park Junpyo's Website

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