Bulletin of Mathematical Biology

, Volume 49, Issue 5, pp 597–613 | Cite as

Theoretical study of a two-dimensional autocatalytic model for calcium dynamics at the extracellular fluid-bone interface

  • P. Tracqui
  • A. M. Perault-Staub
  • G. Milhaud
  • J. F. Staub


The temporal behaviours of the nonlinear substructure of a self-organized compartmental model of calcium metabolism were investigated. The order-two autocatalytic process included in this simple two-dimensional model is compared to some secondary nucleation mechanisms which should take place at the extracellular fluid-bone interface. The model gives rise to complex dynamic behaviours, and multistability properties, involving up to two stable periodic regimes (birhythmicity), were established in different topological configurations. The bifurcations occurring on the boundaries between regions of different qualitative behaviour have been determined. These properties are discussed in relation to the dynamical behaviour of other two-variable models, especially those including the same nonlinearity.


Hopf Bifurcation Bifurcation Diagram Continuous Stir Tank Reactor Stable Limit Cycle Global Bifurcation 
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Copyright information

© Society for Mathematical Biology 1987

Authors and Affiliations

  • P. Tracqui
    • 1
  • A. M. Perault-Staub
    • 1
  • G. Milhaud
    • 1
  • J. F. Staub
    • 1
  1. 1.C.H.U. Saint-AntoineC.N.R.S. UA 163, Service de BiophysiqueParis Cedex 12France

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