Hopf bifurcations in complex multiagent activity: the signature of discrete to rhythmic behavioral transitions

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Most human actions are composed of two fundamental movement types, discrete and rhythmic movements. These movement types, or primitives, are analogous to the two elemental behaviors of nonlinear dynamical systems, namely, fixed-point and limit cycle behavior, respectively. Furthermore, there is now a growing body of research demonstrating how various human actions and behaviors can be effectively modeled and understood using a small set of low-dimensional, fixed-point and limit cycle dynamical systems (differential equations). Here, we provide an overview of these dynamical motor primitives and detail recent research demonstrating how these dynamical primitives can be used to model the task dynamics of complex multiagent behavior. More specifically, we review how a task-dynamic model of multiagent shepherding behavior, composed of rudimentary fixed-point and limit cycle dynamical primitives, can not only effectively model the behavior of cooperating human co-actors, but also reveals how the discovery and intentional use of optimal behavioral coordination during task learning is marked by a spontaneous, self-organized transition between fixed-point and limit cycle dynamics (i.e., via a Hopf bifurcation).

Original languageEnglish
Article number536
Pages (from-to)1-18
Number of pages18
JournalBrain Sciences
Issue number8
Publication statusPublished - Aug 2020

Bibliographical note

Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • multiagent coordination
  • Hopf-bifurcation
  • dynamical motor primitives
  • behavioral dynamics
  • task dynamics
  • shepherding dynamics;
  • synergies


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