Anisotropy and Antagonism in the Coupling of Two Oscillators: Concepts and Applications for Between-Person Coordination

Abstract

Coupled oscillators provide a pertinent model approach to study between-person movement dynamics. While ample literature in this respect has considered the influence of external/environmental constraints and/or effects of a difference between the two agents' individual component dynamics (e.g., mismatch in natural frequency), recent studies also started to more directly consider the interaction per-se. The current perspective paper sets forth that while movement coordination dynamics has mainly been studied alongside a model in which the coupling is considered isotropic (i.e., symmetrical; both oscillators coupled to same degree) or strictly unidirectional (e.g., for moving to a given external rhythm), between-agent coupling involves a natural anisotropy: components influence each other bidirectionally to different degrees. Furthermore, recent research from different areas has considered so-called antagonistic or “competitive” coupling, which refers to the idea that one component is positively coupled to the other (attractive interaction), while the coupling in the other direction is negative (repulsive interaction). Although the latter would be rather tricky to address in within-person coordination, it does have strong applications and implications for between-person dynamics, for instance in the study of competitive interactions in sports situations (e.g., attacker-defender) and conflicting social (movement) interactions. The paper concludes by offering a conceptual framework and perspectives for future studies on the dynamic anisotropic nature of the interaction in between-person contexts.

A Re-Appraisal of the Effect of Amplitude on the Stability of Interlimb Coordination Based on Tightened Normalization Procedures

“…In this respect it is interesting to mention that mathematically it has been shown that for in-phase coordination process 1 is a main mediator and for antiphase it is actually both 1 and 2 (e.g., [ 53 ]), which would indeed be in line with the currently obtained difference between in-phase and antiphase in terms of their frequency-related dynamics. Importantly, this explanation would entail that coupling parameters actually change as a function of time and behavior [ 3 ], whereas in the vast majority of pertinent studies the coupling parameters are assumed to be constant. The possibility of having time-varying coupling parameters constitutes a challenge for both further theoretical and empirical analysis.…”

“…Rhythmical interlimb behavior is thereby characterized by attraction to a limited number of stable coordination patterns [ 1 , 2 ]. Stable interlimb coordination occurs by virtue of the coupling between the components involved: When there is no interaction between limb movements there can be no attraction towards synchronized/coordinated patterns (e.g., [ 2 , 3 ]). Empirically, this is evidenced by the existence of certain stable and hence preferred modes of interlimb coordination in animals and humans [ 1 , 4 ].…”

“…This phenomenon was formalized in the influential Haken–Kelso–Bunz (HKB) model [ 2 ], which consists of a potential function (or gradient dynamics) for relative phase and a system of coupled oscillators underlying the gradient dynamics of relative phase. An entire research program for studying interlimb (e.g., [ 1 , 7 , 8 , 9 ]), sensorimotor (e.g., [ 1 , 10 , 11 , 12 , 13 ]), and between-person (e.g., [ 1 , 3 , 14 , 15 ]) coordination has been built on the HKB model, which has become a cornerstone of coordination dynamics.…”

Complex Systems in Sport, International Congress: Linking Theory and Practice

“…Interestingly, it is also possible to model repulsive coupling. Particularly relevant for sports, implementing competitive coupling between the model oscillators (i.e., one oscillator attracts while the other repels) reflects defender-attacker coupling and may yield patterns that contrast to the generally observed in-and antiphase attraction (Kelso et al, 2009;De Poel, 2016).…”

Coordination Dynamics: A Foundation for Understanding Social Behavior

“…With the simple paradigm of two people moving their fingers back and forth in view of one another, we are able to obtain continuous state variables describing the trajectory of each participant's effector at the behavioral level, their coordination dynamics (viz. the relative phase between the two finger movements, see "Order parameter" below; Tognoli et al, 2007;Oullier et al, 2008;Tognoli, 2008; see also Schmidt et al, 1990Schmidt et al, , 2011Richardson et al, 2007;Schmidt and Richardson, 2008;Marsh et al, 2009;Janata et al, 2012;Reddish et al, 2013;Fine and Amazeen, 2014;Fusaroli et al, 2014;Keller et al, 2014;Tschacher et al, 2014;de Poel, 2016;Moreau et al, 2016; for a variety of related approaches). Further, when expanding this work, information can be gained about concomitant activities in the brain (Tognoli et al, 2007;Jantzen et al, 2008;Naeem et al, 2012; see also Hari and Kujala, 2009;Dumas et al, 2011;Sänger et al, 2011;Konvalinka and Roepstorff, 2012;Pfeiffer et al, 2013;Babiloni and Astolfi, 2014;Cacioppo et al, 2014;Hirata et al, 2014;D'Ausilio et al, 2015;Koike et al, 2015;Zhou et al, 2016;Kawasaki et al, 2018;Mu et al, 2018;Pezzulo et al, 2019), and in emotional subsystems (e.g., Zhang et al, 2016; see also Anders et al, 2011;Balconi and Vanutelli, 2017;…”