Mutual and asynchronous anticipation and action in sports as globally competitive and locally coordinative dynamics

Abstract

Humans interact by changing their actions, perceiving other’s actions and executing solutions in conflicting situations. Using oscillator models, nonlinear dynamics have been considered for describing these complex human movements as an emergence of self-organisation. However, these frameworks cannot explain the hierarchical structures of complex behaviours between conflicting inter-agent and adapting intra-agent systems, especially in sport competitions wherein mutually quick decision making and execution are required. Here we adopt a hybrid multiscale approach to model an attack-and-defend game during which both players predict the opponent’s movement and move with a delay. From both simulated and measured data, one synchronous outcome between two-agent (i.e. successful defence) can be described as one attractor. In contrast, the other coordination-breaking outcome (i.e. successful attack) cannot be explained using gradient dynamics because the asymmetric interaction cannot always assume a conserved physical quantity. Instead, we provide the asymmetric and asynchronous hierarchical dynamical models to discuss two-agent competition. Our framework suggests that possessing information about an opponent and oneself in local-coordinative and global-competitive scale enables us to gain a deeper understanding of sports competitions. We anticipate developments in the scientific fields of complex movement adapting to such uncontrolled environments.

Automatically recognizing strategic cooperative behaviors in various situations of a team sport

“…Studies into artificial multi-agents [12–15] have primarily focused on methods to realize the desired collective movements (i.e., a forward problem). However, multi-agent systems, particularly groups of living organisms, show various and intelligent movements wherein the dominance law is sometimes unclear [16, 17]. If we can classify the complex and functional behavior from data (i.e., an inverse problem), this may promote the understanding of functions of strategic cooperation.…”

Physically-interpretable classification of biological network dynamics for complex collective motions

“…However, a general quantitative validation method for the unknown dynamics is further required. Another is to reflect the more local interaction dynamics such as local competitive and cooperative play by the attackers and defenders [49,50,51,22], which can provides more practical information in the sport domain. Although the purpose of Graph DMD is to extract the underlying global dynamics of GDSs and we can obtain the interpretable local spectra in the DMD modes, there are other approaches for extracting the more specific local dynamics.…”

Data-driven spectral analysis for coordinative structures in periodic systems with unknown and redundant dynamics

“…Actually, walking is sometimes not an ideal cyclic motion; thus we need a method adapting to rhythm shift and perturbation (observed as a phase reset in [47,50,48] and a phase locking in [49]). Our approach can theoretically describe an asymptotic phase in asymptotically stable dynamical systems [38,36]; therefore, it will be possible to apply it to the perturbed or more complicated locomotion [62,63]. Third is the variation within/among participants.…”