The Hindmarsh–Rose modelHindmarsh-Rose model is a system of three nonlinear differential equations that emulates the behavior of neuronsNeurons in terms of their action potentials and firing dynamics. This dimensionless model is designed to capture the complex phenomena of action potentials. In this document, an analysis is performed using transfer functions to gain insight into the system’s stability and how it responds to different inputs. Additionally, the system’s behavior is analyzed through BodeBode plots, which show both the system’s gain and phase in response to variations in input frequency. BodeBode plots allow for identifying resonance points and the stability behavior of the HR model in different regimes. This analysis provides a useful tool for adjusting model parameters in experimental studies or computational simulations. It is particularly relevant for research in computational neuroscience and the creation of accurate models of neuronal activity.

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Frequency Analysis of Neuronal Dynamics in Neural Models

  • A. Macías-Carlos,
  • A. L. Valadez-Ramos,
  • V. A. Pérez-Vital,
  • R. Hernández-Vargas,
  • A. Montes-Vacio,
  • M. H. Hernández-Olvera,
  • R. Velázquez,
  • H. E. Gilardi-Velázquez,
  • A. Ruiz-Silva

摘要

The Hindmarsh–Rose modelHindmarsh-Rose model is a system of three nonlinear differential equations that emulates the behavior of neuronsNeurons in terms of their action potentials and firing dynamics. This dimensionless model is designed to capture the complex phenomena of action potentials. In this document, an analysis is performed using transfer functions to gain insight into the system’s stability and how it responds to different inputs. Additionally, the system’s behavior is analyzed through BodeBode plots, which show both the system’s gain and phase in response to variations in input frequency. BodeBode plots allow for identifying resonance points and the stability behavior of the HR model in different regimes. This analysis provides a useful tool for adjusting model parameters in experimental studies or computational simulations. It is particularly relevant for research in computational neuroscience and the creation of accurate models of neuronal activity.