Bulletin of Mathematical Biology

, Volume 41, Issue 2, pp 193–201 | Cite as

Self-organization in biological systems with multiple cellular contacts

  • A. Babloyantz
  • L. K. Kaczmarek


The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.


Saddle Point Periodic Boundary Condition Spatiotemporal Pattern Linear Stability Analysis Temporal Periodicity 
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Copyright information

© Society for Mathematical Biology 1979

Authors and Affiliations

  • A. Babloyantz
    • 1
  • L. K. Kaczmarek
    • 2
  1. 1.Service de Chimie Physique 2, Faculté des SciencesUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Division of BiologyCalifornia Institute of TechnologyPasadenaU.S.A.

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