Search results for: TIKHONOV THEOREM

• Partial hyperbolicity and central shadowing

  Publication

  • S. Kryzhevich
  • S. Tikhomirov

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS - Year 2013

  We study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.

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• Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein

  Publication

  • A. Bartłomiejczyk
  • M. Bodnar

  - Communications in Nonlinear Science and Numerical Simulation - Year 2020

  We analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three, possibly different, time scales connected with: (i) the process of binding to/dissolving from a binding site, (ii) formation and dissociation of dimers, (iii) production and degradation of Hes1...

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