Research Highlights

The research field is Evolutionary dynamics based on evolutionary games that provides mathematical guidelines to explain complex phenomena in various systems of biological, ecological, and social sciences. Currently, the main frameworks for our works are 1) Cyclic competition, which is generally described by Rock-Paper-Scissors (RPS) game, and 2) Cooperation game that helps to understand social dilemmas. In particular, our current research focuses on dynamical phenomena in systems of evolutionary dynamics from aspects of nonlinear dynamics. In addition, we also try to develop evolutionary game-based models incorporating mathematics and other interdisciplinary fields to realize various phenomena.  Within such research interests, the representative issues are:

and some highlighting issues are introduced below.

(2013) Persistent coexistence in the rock-paper-scissors 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).

(2017) Unusual coexistence in cyclic competition systems by symmetry-breaking of intraspecific competition

Asymmetry is natural and a universal characteristic of the population in real systems. We investigated how symmetry-breaking of intraspecific competition can affect biodiversity in systems of cyclic competition. Intraspecific competition is suggested as a key role to promote species coexistence in rock-paper-scissors games. We consider the nonuniform intraspecific competition in three standard systems of cyclic competition and found that symmetry-breaking can lead to various survival states, which are classified by the number of surviving species. According to the presence of intraspecific competition, the associated linear stability analysis is also changed and biodiversity is robust regardless of mobility.

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

(2018) New approach for mutation in the rock-paper-scissors game

Mutation, a rare but important mechanism, has been introduced in the system of cyclic competition by means of a transition way between two groups. We defined the mutation in a different way to previous approaches that mutation can yield the born of mutant species. Under this consideration, the system can involve six different species when all species can coexist and the interplay between two groups is characterized through mathematical analysis and numerical simulations, which are eventually well-matched.

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

(2018) Emergence of multistability in the rock-paper-scissors system

Classic RPS game-based systems usually fall into the class of Hopf bifurcation, which is supercritical. Thus systems always exhibit only one attractor under given conditions. Such a characteristic can be changed by considering additional mechanisms. We investigated the system which is engaging intraspecific competition of nonlinear form (depending on each group scale) and found the emergence of multistability between a heteroclinic cycle and a sink. It is also found the system has subcritical Hopf bifurcation when multistability occurs.

J. Park, Y. Do, and B. Jang, ``Multistability in the cyclic competition system," Chaos 28, 113110 (2018).

(2019) Balance effects between different pathways of interspecific competition on biodiversity in the rock-paper-scissors-lizard-spock system

An original structure of rock-paper-scissors-lizard-spock game has two distinct pathways of interspecific competition. While the corresponding mean-field system can address three possible states for biodiversity, the heteroclinic cycle associated to the extinction state can only appear. On spatially extended systems, however, we found that, depending on the strengths of two interspecific competitions, the spatial dynamics exhibit an interesting feature on biodiversity with emerging coexistence of all species again at high mobility regime.

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

(2021) Coexistence and intriguing dynamics mediated by RPS competition and environments

Considering environments have been generally regarded in spatial dynamics. We challenged to describe the mechanism of environments by means of the mean-field system of rate equations and found such environmental effect can lead to complex dynamics in the three species system.

M. H. Mohd and J. Park, ``The interplay of rock-paper-scissors competition and environments mediates species coexistence and intriguing dynamics," Chaos, Solitons and Fractals 153, 111579 (2021).

(2022) Correlation between the number of competing groups and spatial scale for biodiversity

Classic studies in cyclic competition systems always consider that the number of different species (or groups) is initially fixed. On the other hand, according to mutation, the system can have additional species than the initial setting, and hence, the dynamics of systems can be changed. In particular, such features can be observed obviously on spatially extended systems. We established the correlation between the number of competing groups and spatial scale for biodiversity in the RPS system with mutation.

J. Park, ``Correlation between the formation of new competing group and spatial scale for biodiversity in the evolutionary dynamics of cyclic competition," Chaos 32, 081101 (2022).

(2023) Various collective behavior of species coexistence under adaptive intraspecific competition

Species coexistence usually appear as spiral entanglement on spatially extended systems in classic systems of cyclic competition. When intraspecific competition occurs, however, strong competition can make species self-survival, and spirally entangled patterns can be broken. As such intraspecific competition occurs adaptively further, coexistence still can occur even if mobility is high, and they form plane waves that describe species as united in the same group, and such features can be accompanied by the nonmonotonic behavior in the extinction probability.

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) Common dynamics in biodiversity of cyclic competition systems among multispecies

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. By implementing subgroup structures, the reason for maintaining or breaking cascading dynamics is uncovered, and the result may provide a piece of evidence to predict biodiversity in complex species systems.

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).