HODGKIN HUXLEY MODEL AND BIFURCATIONS IN THE MORRIS-LECAR MODEL

Abstract

This thesis examines mathematical models in neuroscience, focusing on the Hodgkin-Huxley and Morris-Lecar models to understand the dynamics of neuronal activities. It explores the voltage-clamp technique pivotal for understanding ionic currents across neuronal membranes, leading to groundbreaking insights into how action potentials are initiated and propagated. With a detailed analysis, this thesis dissects these foundational models, introducing modifications that align more closely with observed biological phenomena. By employing bifurcation theory, it examines the transition between different neuronal firing patterns, providing a rich theoretical framework for understanding the complex behaviors of neurons under various stimuli.