Chaotic Synchronization and Damage Detection
Author:
Sethumte Asamoah-Nani ’26Co-Authors:
Faculty Mentor(s):
Professor Andrew SlobodaFunding Source:
Emerging Scholars GrantAbstract
The general approach to the research was to attempt to build as much knowledge on chaotic systems and synchronization as possible in order to explore potential avenues for future research. Seeing as I was unfamiliar with the code and I needed to simulate the relevant chaotic systems, an introductory course to that syntax was one of the initial aims of the research. Familiarizing myself with differential equation calculations as well as various ways of displaying and interpreting the relevant data were essential skills I picked up in the wee stages of this research.
A literature review of relevant papers followed the introductory phase of the research where I looked for, read, and summarized salient aspects of academic articles in relation to chaotic synchronization and damage detection. Now armed with relevant information, skills, and equations I began to replicate previous works cited in articles in order to reconcile all the various skills I had annexed over the weeks and cement my understanding of them as a single analytical procedure.
I mostly worked in MATLAB and relied on the advanced integral calculator ODE45 to run most of my simulations. By simulating appropriately coupled chaotic systems I attempted to see if I could determine the difference between parameter values in the equations of the two involved systems (damage). I did this by evaluating one of the output component’s clearly defined properties. The result was that I found two ways of reliably determining the value of unknown parameters in the driving equation by comparing the output values:
1)The value of the deviation in the first peak or trough from the start line
2)The average of one of the predetermined outputs of the system
While the results varied for different chaotic systems, in most cases one or the other or both gave a good estimation of the value.
Aside from these findings I learned a few new math-oriented skills like how to calculate eigenvalues and determine the nature of a chaotic system based off it, how to write a state space equation and how to plot vector fields in MATLAB.