Perspectives on multi-level dynamics

Fatihcan M. Atay, Sven Banisch, Philippe Blanchard, Bruno Cessac, Eckehard Olbrich, Dima Volchenkov

Research output: Contribution to journalArticlepeer-review


As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters, linked together by causal equations of evolution whose structure may reveal hidden principles. This requires a huge reduction of dimensionality (number of degrees of freedom) and a change in the level of description. Beyond the mere necessity of developing accurate tech niques affording this reduction, there is the question of the correspondence between the initial system and the reduced one. In this paper, we offer a perspective towards a common framework for discussing and understand ing multi-level systems exhibiting structures at various spatial and temporal levels. We propose a common foundation and illustrate it with examples from different fields. We also point out the difficulties in constructing such a general setting and its limitations.

Original languageEnglish
Pages (from-to)313-339
Number of pages27
JournalDiscontinuity, Nonlinearity, and Complexity
Issue number3
StatePublished - 2016


  • Hierarchy of levels
  • Multi-level dynamical systems
  • Reduction of dimensionality
  • Scales and levels


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