{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:47:16Z","timestamp":1785545236780,"version":"3.56.0"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,10]]},"abstract":"<jats:p> Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in which the number of variables is usually small enough for analysis. The dynamical images of different mental processes depend on their temporal organization and, as a rule, cannot be just simple attractors since cognition is characterized by transient dynamics. The mathematical image for a robust transient is a stable heteroclinic channel consisting of a chain of saddles connected by unstable separatrices. We focus here on hierarchical chunking dynamics that can represent several cognitive activities. Chunking is the dynamical phenomenon that means dividing a long information chain into shorter items. Chunking is known to be important in many processes of perception, learning, memory and cognition. We prove that in the phase space of the model that describes chunking there exists a new mathematical object \u2014 heteroclinic sequence of heteroclinic cycles \u2014 using the technique of slow\u2013fast approximations. This new object serves as a skeleton of motions reflecting sequential features of hierarchical chunking dynamics and is an adequate image of the chunking processing. <\/jats:p>","DOI":"10.1142\/s0218127414501326","type":"journal-article","created":{"date-parts":[[2014,10,31]],"date-time":"2014-10-31T01:52:45Z","timestamp":1414720365000},"page":"1450132","source":"Crossref","is-referenced-by-count":10,"title":["Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking"],"prefix":"10.1142","volume":"24","author":[{"given":"Valentin S.","family":"Afraimovich","sequence":"first","affiliation":[{"name":"Institute de Investigacion Communicasion Optica, Universidad Aut\u00f3noma de San Luis Potos\u00ed, A. Obregon, 7800, SLP, San Luis Potos\u00ed, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Todd R.","family":"Young","sequence":"additional","affiliation":[{"name":"Mathematics Department, Ohio University, 321 Morton Hall, Athens, OH 45701, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail I.","family":"Rabinovich","sequence":"additional","affiliation":[{"name":"BioCircuits Institute, University of California, San Diego, 9500 Gilman Dr., #0328, LaJolla, CA 92093, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2014,10,30]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","DOI":"10.1090\/amsip\/028","volume-title":"Lectures on Chaotic Dynamical Sytems","volume":"28","author":"Afraimovich V. 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