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A coupled inverted pendula model of competition and cooperation is proposed to develop a purely mechanical implementation comparable to the Lotka-Volterra competition model. It is shown numerically that the proposed model can produce the four stable equilibriums analogous to ecological coexistence, two states of dominance, and scramble. The authors also propose two types of open-loop strategies to switch the equilibriums. The proposed strategies can be associated with an attack and a counter attack of agents through a metaphor of martial arts.

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In this study, we propose a new simple degree-of-freedom fluctuation model that accurately reproduces the probability density functions (PDFs) of human–bicycle balance motions as simply as possible. First, we measure the time series of the roll angular displacement and velocity of human–bicycle balance motions and construct their PDFs. Next, using these PDFs as training data, we identify the model parameters by means of particle swarm optimization; in particular, we minimize the Kolmogorov–Smirnov distance between the human PDFs from the participants and the PDFs simulated by our model. The resulting PDF fitnesses were over 98.7 % for all participants, indicating that our simulated PDFs were in close agreement with human PDFs. Furthermore, the Kolmogorov–Smirnov statistical hypothesis testing was applied to the resulting human–bicycle fluctuation model, showing that the measured time responses were much better supported by our model than the Gaussian distribution.