Behavior Research Methods

, Volume 50, Issue 1, pp 182–194 | Cite as

A flexible and accurate method to estimate the mode and stability of spontaneous coordinated behaviors: The index-of-stability (IS) analysis

  • Gregory Zelic
  • Deborah Varoqui
  • Jeesun Kim
  • Chris Davis


Patterns of coordination result from the interaction between (at least) two oscillatory components. This interaction is typically understood by means of two variables: the mode that expresses the shape of the interaction, and the stability that is the robustness of the interaction in this mode. A potent method of investigating coordinated behaviors is to examine the extent to which patterns of coordination arise spontaneously. However, a prominent issue faced by researchers is that, to date, no standard methods exist to fairly assess the stability of spontaneous coordination. In the present study, we introduce a new method called the index-of-stability (IS) analysis. We developed this method from the phase-coupling (PC) analysis that has been traditionally used for examining locomotion–respiration coordinated systems. We compared the extents to which both methods estimate the stability of simulated coordinated behaviors. Computer-generated time series were used to simulate the coordination of two rhythmic components according to a selected mode m:n and a selected degree of stability. The IS analysis was superior to the PC analysis in estimating the stability of spontaneous coordinated behaviors, in three ways: First, the estimation of stability itself was found to be more accurate and more reliable with the IS analysis. Second, the IS analysis is not constrained by the limitations of the PC analysis. Third and last, the IS analysis offers more flexibility, and so can be adapted according to the user’s needs.


Spontaneous entrainment Frequency-locking Phase-coupling Stability Method 

Supplementary material

13428_2017_861_MOESM1_ESM.docx (33 kb)
S1 Appendix The phase-coupling (PC) analysis. (DOCX 32 kb)
13428_2017_861_MOESM2_ESM.docx (24 kb)
S2 Appendix Limitations of the PC analysis. (DOCX 24 kb)
13428_2017_861_MOESM3_ESM.docx (26 kb)
S3 Appendix The index-of-stability (IS) analysis. (DOCX 26 kb)
13428_2017_861_MOESM4_ESM.docx (24 kb)
S4 Appendix The circle map model. (DOCX 23 kb)
13428_2017_861_MOESM5_ESM.docx (62 kb)
S5 Appendix MATLAB scripts/functions. (DOCX 62 kb)


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Copyright information

© Psychonomic Society, Inc. 2017

Authors and Affiliations

  • Gregory Zelic
    • 1
  • Deborah Varoqui
    • 2
  • Jeesun Kim
    • 1
  • Chris Davis
    • 1
  1. 1.The MARCS InstituteWestern Sydney UniversitySydneyAustralia
  2. 2.EuromovUniversity of MontpellierMontpellierFrance

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