Research Highlights

(2013) Persistent coexistence in the RPS system by habitat suitability

We revisited a milestone work in the field of cyclic competition by engaging habitat suitability index (HSI) into species migration. Under assuming migration (or an exchange motion between two neighboring sites on a square lattice) is sensitive to HSI, we find that the coexistence of species can be promoted, and persistent coexistence appears even at high mobility regimes. Coexisting species are globally distributed rather than spirally entangled, and the portion of empty sites is relatively higher than species density at the same time.

J. Park, Y. Do, Z.-G. Huang, and Y.-C. Lai, ``Persistent coexistence of cyclically competing species in spatially extended ecosystems," Chaos 23, 023128 (2013).

(2016-2023) Symmetry-breaking of interactions in cyclic competition systems

Asymmetry is natural and a universal characteristic of the population in real systems. In this regard, symmetry-breaking of interactions may affect species biodiversity in cyclic competition systems, and may play a key role. About this topic, we focused on various mechanisms encompassing intraspecific competition, mutation, and adaptive competition.

J. Park, Y. Do, B. Jang, and Y.-C. Lai, ``Emergence of unusual coexistence states in cyclic game systems," Scientific Reports 7, 7465 (2017).

J. Park, ``Biodiversity in the cyclic competition system of three species according to the emergence of mutant species," Chaos 28, 053111 (2018).

J. Park and B. Jang, ``Robust coexistence with alternative competition strategy in the spatial cyclic game of five species," Chaos 29, 051105 (2019).

J. Park and B. Jang, ``Role of adaptive intraspecific competition on collective behavior in the rock-paper-scissors game," Chaos, Solitons and Fractals 171, 113448 (2023).

(2023-2027) Mathematical insights on cascading dynamics and higher-order interactions in cyclic game systems

Classic systems of cyclic competitions governed by RPS or RPSLS games exhibit cascading dynamics that biodiversity changes with a certain decreasing relation via mobility. This research identifies that cascading behavior still occurs even when we consider multispecies groups are given. In addition, even if the number of multigroups is the same, changing pathways of interspecific competition (selection or predation) can also affect biodiversity, and hence, cascading behavior cannot be predicted. In this regard, utilizing directed graph representations and theory of tournaments, we identified the mechanism of ecological cascading in cyclic game systems. We further explore how higher-order interaction, one of the recent key issues, can affect evolution of systems, and reveal out its significant role in biodiversity.

J. Park, X. Chen, and A. Szolnoki, ``Competition of alliances in a cyclically dominant eight-species population," Chaos, Solitons and Fractals 166, 113004 (2023).

R. K. Yang and J. Park, ``Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity," Chaos, Solitons and Fractals 175, 113949 (2023).

Y. Lu, X. Wang, C. Du, Y. Wang, Y. Geng, L. Shi, and J. Park, ``Understanding the role of neutral species by means of high-order interaction in the rock-paper-scissors dynamics," Physical Review E 109, 014313 (2024).

R. K. Yang, S. Hong, S. Kim, and J. Park, ``Understanding ecological cascade in cyclic game systems by means of directed graphs," Chaos 35, 111101 (2025).