Wyniki wyszukiwania dla: neuronal dynamics, β-transformations, farey-lorenz permutations, periodic spiking, chaos

• Analysis of dynamics of a map-based neuron model via Lorenz maps

  Publikacja

  • P. Bartłomiejczyk
  • F. Llovera Trujillo
  • J. Signerska-Rynkowska

  - CHAOS - Rok 2024

  Modeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...

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• Periodic and chaotic dynamics in a map‐based neuron model

  Publikacja

  • F. Llovera Trujillo
  • J. Signerska-Rynkowska
  • P. Bartłomiejczyk

  - MATHEMATICAL METHODS IN THE APPLIED SCIENCES - Rok 2023

  Map-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...

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• Spike patterns and chaos in a map-based neuron model

  Publikacja

  • P. Bartłomiejczyk
  • F. Llovera Trujillo
  • J. Signerska-Rynkowska

  - International Journal of Applied Mathematics and Computer Science - Rok 2023

  The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....

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• Dold sequences, periodic points, and dynamics

  Publikacja

  • J. Byszewski
  • G. Graff
  • T. Ward

  - BULLETIN OF THE LONDON MATHEMATICAL SOCIETY - Rok 2021

  In this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.

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• CHAOS

  Czasopisma

  ISSN: 1054-1500 , eISSN: 1089-7682

• Hysteresis curves for some periodic and aperiodic perturbations in gases

  Publikacja

  • A. Perelomova

  - CANADIAN JOURNAL OF PHYSICS - Rok 2014

  Evolution of sound in a medium whose properties irreversibly vary in the course of wave propagation, is studied. For example, a gas that is a particular case of a Newtonian fluid is considered. Hysteresis curves, pictorial representations of irreversible attenuation of the sound energy, in the plane of thermodynamic states are plotted. The irreversible losses in internal energy are proportional to the total attenuation and depend...

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• Acoustic Streaming Induced by Periodic and Aperiodic Sound in a Bubbly Liquid

  Publikacja

  • P. Wojda
  • A. Perelomova

  - ACTA PHYSICA POLONICA A - Rok 2014

  The vortex ow which follows intense sound propagating in a bubbly liquid, is considered. The reasons for acoustic streaming are both nonlinearity and dispersion. That makes streaming especial as compared with that in a Newtonian uid. Conclusions concern the vortex ow induced in a half-space by initially harmonic or impulse Gaussian beam. The vortex ow recalls a turbulent ow with increasing in time number of small-scale vortices...

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• Hysteresis curves for some periodic and aperiodic perturbations in magnetosonic flow

  Publikacja

  • A. Perelomova

  - PHYSICS OF PLASMAS - Rok 2020

  A thermodynamic relation between perturbations of pressure and mass density in the magnetohydrodynamic flow is theoretically studied. Planar magnetohydrodynamic perturbations with the wave vector, which forms a constant angle with the equilibrium magnetic field, are under study. The theory considers thermal conduction of a plasma and the deviation from adiabaticity of a flow due to some kind of heating–cooling function. It also...

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• Dynamics study on single and multiple β-sheets

  Publikacja

  • I. Liepina
  • S. Ventura
  • C. Czaplewski
  • A. Liwo

  - Rok 2009

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• Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid

  Publikacja

  • P. Wojda

  - Rok 2012

  This paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...