Equilibrium locus of the flow on circular networks of cells

Yirmeyahu J. Kaminski

Research output: Contribution to journalArticlepeer-review


We perform a geometric study of the equilibrium locus of the ow that models the diffiusion process over a circular network of cells. We prove that when considering the set of all possible values of the parameters, the equilibrium locus is a smooth manifold with corners, while for a given value of the parameters, it is an embedded smooth and connected curve. For different values of the parameters, the curves are all isomorphic. Moreover, we show how to build a homotopy between different curves obtained for different values of the parameter set. This procedure allows the efficient computation of the equilibrium point for each value of some first integral of the system. This point would have been otherwise difficult to be computed for higher dimensions. We illustrate this construction by some numerical experiments. Eventually, we show that when considering the parameters as inputs, one can easily bring the system asymptotically to any equilibrium point in the reachable set, which we also easily characterize.

Original languageEnglish
Pages (from-to)1169-1177
Number of pages9
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue number6
StatePublished - Dec 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.


  • Equilibrium
  • Fiber spaces
  • Homotopy continuation


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