Nonlinear dynamics in Neuroscience

Graduate course
  Taught at: 2020, 2024
  Latin American School on Computational Neuroscience - LASCON, Universidade de São Paulo (USP)

Explore the connection of dynamical systems in neural modeling. Delve into reduced one- and two-dimensional neural models, examining their intricacies and behavior in phase-space analysis. Uncover the phenomena of subthreshold oscillations, the canard phenomenon, and resonance, both subthreshold and suprathreshold. The course also delves into the intriguing dynamics of bursting in neural systems.


  • Understand the fundamentals of dynamical systems and their applications in neural modeling.
  • Analyze reduced one-dimensional neural models using phase-space analysis.
  • Explore the phase-space analysis of two-dimensional neural models.
  • Examine subthreshold oscillations and the canard phenomenon in neural systems.
  • Investigate the concepts of subthreshold and suprathreshold resonance in neural dynamics.
  • Gain insights into the dynamics of bursting in neural systems.


  1. Izhikevich E.M. (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT press
  2. Strogatz, S. (2015) Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering. Westview Press