Wyniki wyszukiwania dla: CONLEY INDEX

• An absorbing set for the Chialvo map

  Publikacja

  • P. Pilarczyk
  • G. Graff

  - Communications in Nonlinear Science and Numerical Simulation - Rok 2024

  The classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...

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

  Publikacja

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

  - CHAOS - Rok 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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