The authors present a dynamical multilevel model that captures changes over time in the bidirectional, potentially asymmetric influence of 2 cyclical processes. S. M. Boker and J. Grahams (1998) differential structural equation modeling approach was expanded to the case of a nonlinear coupled oscillator that is common in bimanual coordination studies in which participants swing hand-held pendulums but is also applicable to social systems in general. The authors nonlinear coupled oscillator model decomposed the fluctuations into a competitive component, unique to each individual variable, and a cooperative component that captured bidirectional influence. The authors model also generated an index of the symmetry/asymmetry of bidirectional influence. Together, the models are useful quantitative tools for the study of interacting, changing processes.

Abstract from:

Butner, J., Amazeen, P. G., & Mulvey, G. M. (2005). Multilevel modeling of two cyclical processes: Extending differential structural equation modeling to nonlinear coupled systems. Psychological Methods, 10, 159-177.

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