2005 Student Research Conference:

18th Annual Student Research Conference

18th Annual Student Research Conference

**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