Publications about 'forced oscillations'
Articles in journal or book chapters
  1. E.V. Nikolaev, S.J. Rahi, and E.D. Sontag. Chaos in simple periodically-forced biological models. 2017. Note: Submitted. Preprint: biorxiv 10.1101/145201.[PDF] Keyword(s): chaos, entrainment, systems biology, periodic inputs, subharmonic responses, biochemical systems, forced oscillations.
    What complicated dynamics can arise in the simplest biochemical systems, in response to a periodic input? This paper discusses two models that commonly appear as components of larger sensing and signal transduction pathways in systems biology: a simple two-species negative feedback loop, and a prototype nonlinear integral feedback. These systems have globally attracting steady states when unforced, yet, when subject to a periodic excitation, subharmonic responses and strange attractors can arise via period-doubling cascades. These behaviors are similar to those exhibited by classical forced nonlinear oscillators such as those described by van der Pol or Duffing equations. The lack of entrainment to external oscillations, in even the simplest biochemical networks, represents a level of additional complexity in molecular biology.



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Last modified: Thu Nov 23 10:40:56 2017
Author: sontag.

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