Dynamical systems theory provides a powerful tool for analyzing nonlinear systems of differential equations, including those that arise in neuroscience. This theory allows us to interpret solutions geometrically as curves in a phase space. By studying the geometric structure of phase space, we are often able to classify the types of solutions that a model may exhibit and determine how solutions depend on the model’s parameters. For example, we can often predict if a model neuron will generate an action potential, determine for which values of the parameters the model will produce oscillations, and compute how the frequency of oscillations depends on the parameters.
KeywordsPeriodic Solution Hopf Bifurcation Bifurcation Diagram Phase Plane Unstable Manifold
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