Chaos in the Brain: A Simulation of Coupled Differential Equations

Overview

Objectives/Goals The goal of this project was to effectively and numerically solve coupled differential equations that display chaotic behavior in a computer program. The differential equations modeled the system dynamics of neural firings inside of a human brain. Methods/Materials In order to complete this project, the researcher had to first acquire the programming skill that would be needed in order to write the computer project. The program was written in a language known as #Scheme.# Scheme is a function based language meaning that functions can be passed as parameters. Also the researcher had to learn ways of finding the derivative (slope of a function), integration (area under a function), and numerical methods to solve the differential equations. Results The written computer program returned a graph of the functions. It showed phase trajectories moving towards either of two points. Conclusions/Discussion It is concluded that it is indeed possible to write a computer program to numerically solve coupled differential equations that display chaotic behavior. Two points of attraction, or places where there is stability, were found on the graph. However, a limit cycle was wanted in return rather than the points of attraction. The parameters used must have not been correct in order to form the limit cycle. Another program will be written to explore the possibilities for all of the parameters.

Competition history

• CSEF 2002 Mathematics & Software · Entry S1206

Resources

• CSEF project summary ↗

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