Title of Oral/Poster Presentation

Determining the Chaotic Nature of Periodic Orbits

Presenter Information

Bo Johnson, Utah State University

Class

Article

College

College of Science

Presentation Type

Poster Presentation

Abstract

Using Lyapunov exponents as a measure of chaos in integrable systems, we characterize the chaotic nature of 1243 distinct periodic modes in a two-magnetic dipole system. After finding these distinct modes from previous research we wanted to understand their long-term behavior. We implemented an algorithm to compute the spectrum of Lyapunov exponents for the dipole system, determining the chaotic nature of the orbit by the largest exponent found. The use of Lyapunov exponents for this particular system hasn't yet shown clear results of which orbits are chaotic or not, due to the non-smooth nature of the equations. We are looking at other means of determining chaos with methods such as the Small Alignment Index (SALI) or the Generalized Alignment Index (GALI).

Start Date

4-9-2020 12:00 PM

End Date

4-9-2020 1:00 PM

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Apr 9th, 12:00 PM Apr 9th, 1:00 PM

Determining the Chaotic Nature of Periodic Orbits

Using Lyapunov exponents as a measure of chaos in integrable systems, we characterize the chaotic nature of 1243 distinct periodic modes in a two-magnetic dipole system. After finding these distinct modes from previous research we wanted to understand their long-term behavior. We implemented an algorithm to compute the spectrum of Lyapunov exponents for the dipole system, determining the chaotic nature of the orbit by the largest exponent found. The use of Lyapunov exponents for this particular system hasn't yet shown clear results of which orbits are chaotic or not, due to the non-smooth nature of the equations. We are looking at other means of determining chaos with methods such as the Small Alignment Index (SALI) or the Generalized Alignment Index (GALI).