Search results for: chain recurrence

• Topological-numerical analysis of a two-dimensional discrete neuron model

  Publication

  • P. Pilarczyk
  • J. Signerska-Rynkowska
  • G. Graff

  - CHAOS - Year 2023

  We conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times...

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• Weak forms of shadowing in topological dynamics

  Publication

  • D. Cherkashin
  • S. Kryzhevich

  - Topological Methods in Nonlinear Analysis - Year 2017

  We consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...

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