A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

Abstract

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. As discrete dynamics, return map analysis was applied to the time series of movements during kendo matches, and six coordination patterns were classified. Furthermore, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts.

Combat as an Interpersonal Synergy: An Ecological Dynamics Approach to Combat Sports

“…An effective description of the interactions between combatants requires approaches for capturing both "discrete movement" at the local level (e.g., modelled as "point attractors") and rhythmic action at the global level (e.g., modelled as "limit cycles") [56]. Relating these two levels of analysis is an important scientific challenge in combat sports [57].…”

“…Locallevel behavior (individual athletes stepping towards or away from each other) scales the control parameter up and down, thereby stabilizing or destabilizing the fight at the global level. In further work, Yamamoto et al [57,75] modelled the interactions of kendo combatants as a hybrid dynamical system to characterize both discrete (stepping maneuvers and striking opportunities) and cyclical behaviors (preferred interpersonal distances and velocities for attacking and defense). This hybrid system comprises both a higher, discrete module and a lower, continuous module connected through a feedback loop, which allows for "very complex, diverse, continuous human movement" [75, p. 6].…”

“…For example, Hristovski et al [5] noted that, in boxing, besides interpersonal distance "other constraints like the defensive position of the arms of the opponent may regulate the attacker's intentions in specific ways which requires further investigation" (p. 61). We expect that approaches examining the probabilities of different affordances at fixed points (e.g., such as examining state transition probabilities [57]) can reveal insights into the constraints on the emergence of affordances during combat. This should highlight important information sources for supporting emergent goals and, subsequently, how information sources may need to vary.…”