Incorporating randomness is critical in mathematical modeling to best represent real-life phenomena, especially in the biological space. A common strategy to best capture these complex dynamics is to operate inside a stochastic framework. This project explores extensions of an ordinary differential equation (ODE) system to stochastic differential equations (SDEs), specifically to the Hodgkin-Huxley neuron model. Through numerical approaches such as the Euler-Maruyama (EM) method and the Ensemble Kalman Filter (EnKF), we aim to analyze how the neuron dynamics compare in an ODE vs. SDE structure. Data assimilation techniques are utilized motivated by the potential to apply EM and EnKF methods to inverse problems with real data.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Tierney, Natalie

Subject

• Computing
• Project-Based Learning

Publisher

• Worcester Polytechnic Institute

Identifier

• 122048
• E-project-042924-172143

Mot-clé

• Euler-Maruyama
• stochastic differential equations
• Hodgkin-Huxley neuron model
• state estimation
• ensemble Kalman filter
• inverse problems

Advisor

• Arnold, Andrea N.

Year

• 2024

UN Sustainable Development Goals

• Not Specified

Date created

• 4/29/2024

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Source

• E-project-042924-172143

Rights statement

• In Copyright