About the Authors

Masaya Hirashima

hira@p.u-tokyo.ac.jp

Affiliation Division of Physical and Health Education, Graduate School of Education, The University of Tokyo, Bunkyo-ku, Tokyo, Japan

Daichi Nozaki

Affiliation Division of Physical and Health Education, Graduate School of Education, The University of Tokyo, Bunkyo-ku, Tokyo, Japan

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Analyzed the data: MH. Contributed reagents/materials/analysis tools: MH. Wrote the paper: MH DN. Conceived and designed the simulations: MH. Performed the simulations: MH. Mathematically proved the convergence of the equations: MH DN.