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.

Objectives

• 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.

Bibliography

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