18th Annual Student Research Conference
Science
Exploring Regions of "Chaos" in the Logistic Map
Cameron C. Moore
Dr. Michael Goggin, Faculty Mentor
“Short-term” Lyapunov Exponents for the logistic map were calculated using Mathematica. Lyapunov exponents are an indicator of the long term sensitivity of a map to changes in initial conditions; they are calculated using an infinite sum. The “short-term” exponents are finite approximations of the infinite limit, and may be coupled to specific regions of the map. Different parameters, which correspond to regions of coarse-grained periodicity of the logistic map orbit, were explored using the coded functions. Plots were initially made to evaluate the overall “short-term” Lyapunov Exponent for orbits based on the starting x-value. Another function was developed to look at the “short-term” Lyapunov Exponent for points in each of the coarse-grained periodic regions, to measure each region’s contribution to the “chaos” of the overall orbit.
Keywords: chaos
Topic(s):Physics
Presentation Type: Oral Paper
Session: 56-2
Location: VH 1412
Time: 4:00