{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T19:30:45Z","timestamp":1779910245747,"version":"3.53.1"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,10]]},"abstract":"<jats:p> Determination of synchronization phenomena between pairs of coupled multivariate processes is of particular interest in Nonlinear Dynamics. Besides synchronization phenomena, coupling directions between the processes are investigated. We present an approach to analyze coupling directions in multivariate oscillatory stochastic systems. We propose usage of partial directed coherence developed in the framework of linear stochastic processes. We show that partial directed coherence is also applicable to detect coupling directions in nonlinear systems such as coupled stochastic van der Pol and stochastic R\u00f6ssler systems. Furthermore, a differentiation between direct and indirect couplings in multivariate systems is possible when applying partial directed coherence. <\/jats:p>","DOI":"10.1142\/s0218127407019664","type":"journal-article","created":{"date-parts":[[2008,1,15]],"date-time":"2008-01-15T11:02:14Z","timestamp":1200394934000},"page":"3735-3739","source":"Crossref","is-referenced-by-count":11,"title":["DETECTING COUPLING DIRECTIONS IN MULTIVARIATE OSCILLATORY SYSTEMS"],"prefix":"10.1142","volume":"17","author":[{"given":"MATTHIAS","family":"WINTERHALDER","sequence":"first","affiliation":[{"name":"Center for Data Analysis and Modeling, University Freiburg, Eckerstr. 1, 79104 Freiburg, Germany"},{"name":"Bernstein Center for Computational Neuroscience, University Freiburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"BJ\u00d6RN","family":"SCHELTER","sequence":"additional","affiliation":[{"name":"Center for Data Analysis and Modeling, University Freiburg, Eckerstr. 1, 79104 Freiburg, Germany"},{"name":"Bernstein Center for Computational Neuroscience, University Freiburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JENS","family":"TIMMER","sequence":"additional","affiliation":[{"name":"Center for Data Analysis and Modeling, University Freiburg, Eckerstr. 1, 79104 Freiburg, Germany"},{"name":"Bernstein Center for Computational Neuroscience, University Freiburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00007990"},{"key":"rf2","volume-title":"Time Series: Theory and Methods","author":"Brockwell P. J.","year":"1998"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s001840000055"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755743"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(76)90101-8"},{"key":"rf6","author":"Schelter B.","journal-title":"J. Neurosci. Meth."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.81.3291"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1080\/14786442208633932"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2005.07.011"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407019664","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:02:52Z","timestamp":1565136172000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407019664"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10]]},"references-count":9,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,10]]}},"alternative-id":["10.1142\/S0218127407019664"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407019664","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,10]]}}}