Title

Electronic Realization of a Chaotic Differential Equation

Presenter Information

Matthew Ingham

Document Type

Oral Presentation

Location

SURC 140

Start Date

17-5-2012

End Date

17-5-2012

Abstract

An electronic realization of a third order nonlinear ordinary differential equation was designed and built using operational amplifiers, a voltage multiplier integrated circuit, and a variety of other electronic components. The behavior of the circuit was investigated both qualitatively and quantitatively, and modeled using Mathematica. As anticipated, the behavior of the system exhibited both periodic and aperiodic chaotic behavior as indicated by both qualitative examination of the phase space of the system and the spectrum of the largest characteristic Lyapunov exponent. The results of these investigations were used in conjunction with a program implemented in Mathematica to calculate the Lyapunov exponent for the chaotic differential equation for particular values of the control parameter.

Faculty Mentor(s)

Michael Braunstein

Additional Mentoring Department

Physics

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May 17th, 4:10 PM May 17th, 4:30 PM

Electronic Realization of a Chaotic Differential Equation

SURC 140

An electronic realization of a third order nonlinear ordinary differential equation was designed and built using operational amplifiers, a voltage multiplier integrated circuit, and a variety of other electronic components. The behavior of the circuit was investigated both qualitatively and quantitatively, and modeled using Mathematica. As anticipated, the behavior of the system exhibited both periodic and aperiodic chaotic behavior as indicated by both qualitative examination of the phase space of the system and the spectrum of the largest characteristic Lyapunov exponent. The results of these investigations were used in conjunction with a program implemented in Mathematica to calculate the Lyapunov exponent for the chaotic differential equation for particular values of the control parameter.