- Project Background:
The Bonhoeffer-van der Pol Oscillator is a simple mathematical model
of neural activity.
Despite its simplicity, its behavior can be quite complex depending on
the values of the model parameters.
Bifurcations of saddle-node, Hopf, saddle-loop, saddle-node-loop types, and
others have been observed.
- Project Description:
The student would have the opportunity to analyze the Bonhoeffer-van
der Pol equation from a numerical and analytical point of view.
The dual approach of numerics and analysis would be employed to
determine regions in parameter space where the different types of
bifurcations take place.
- Desired Student Background:
Ability to program in a high-level language, preferably Mathematica, C/C++, or FORTRAN, and mathematical background
including linear algebra (the equivalent of MATH 242) and ordinary
differential equations (at the
level of MATH 365).