Exploring Causal Relationships in the Phase Functions of Coupled Van der Pol Oscillators

  • C.J. Cellucci
  • P.E. Rapp
Conference paper


We investigate whether causal relationships in coupled Van der Pol oscillators can be determined. Using the instantaneous phase of computer generated time series, which are unidirectionally and time dependently coupled, the technique of lagged mutual information is tested to determine its usefulness in detecting information transmission. If successful, it could assist in improving our understanding of the role of information transmission in organizing CNS activity.


Mutual Information Physical Review Information Transfer Granger Causality Instantaneous Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Van der Pol, B. Forced oscillations in a circuit with non-linear resistance. Philosophical Magazine 3 (1927) 62–80.Google Scholar
  2. 2.
    Van der Pol, B., Van der Mark, J. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Philosophical Magazine 6 (1928) 763–775.Google Scholar
  3. 3.
    Gabor, D. Theory of communication. Journal of the Institute of Electrical Engineers (London) 93 (1946) 429–457.Google Scholar
  4. 4.
    Schafer, C., Rosenblum, M.G., Abel, H., Kurths, J. Synchronization in the human cardiorespiratory system. Physical Review E 60(1) (1999) 857–869.CrossRefGoogle Scholar
  5. 5.
    Wiener, N. The theory of prediction, In: Beckenback, E.R., (ed.): Modern Mathematics for Engineers. McGraw Hill, New York (1956).Google Scholar
  6. 6.
    Granger, C. W. J. Investigating causal relation by econometric and cross-sectional method. Econometrica 37 (1969) 424–438.CrossRefGoogle Scholar
  7. 7.
    Sims, C.A. Money, income, and causality. The American Economic Review 62 (1972) 540–552.Google Scholar
  8. 8.
    Kaneko, K. Lyapunov analysis and information flow in coupled map lattices. Physica 23D (1986) 436–477.Google Scholar
  9. 9.
    Vastano, J.A., Swinney, H.L. Information transport in spatiotemporal systems, Physical Review E 60 (1988) 1773–1776.Google Scholar
  10. 10.
    Albano, A.M., Bedonie, C., Cellucci, C.J., Halkides, D., Miller, V., Ree, J., Torruella, A., Harner, R.N., Rapp, P.E. Spatiotemporal EEG information transfer in an episode of epilepsy. In: Sreenivasan, R., Pradhan, N. and Rapp, P.E.. (eds.) Nonlinear Dynamics and Brain Functioning. Nova Publishing, NY (1999) 411–434.Google Scholar
  11. 11.
    Schreiber, T. Measuring information transfer. Physical Review Letters 85, (2000) 461–464.PubMedCrossRefGoogle Scholar
  12. 12.
    Cellucci, C.J., Albano, A.M., Rapp, P.E.. Statistical validation of mutual information calculations: comparisons of alternative numerical algorithms. Physical Review E 71(6) (2005) 066208.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • C.J. Cellucci
    • 1
  • P.E. Rapp
  1. 1.Aquinas, LLCBerwynUSA

Personalised recommendations