An Exploration Of The Ueda Oscillator Using Analog Computers To Map The Three Dimensional Phase Space To Two Dimensions: A Look Into The Future Using The Techniques Of The Past

Noah David Johnston

It is possible to model mathematical functions using different electrical components. By using voltage as a variable and these components as functions, it is possible to build an analog computer which models a differential equation. These analog computers, while not as versatile as digital computers, have certain advantages over them especially in the study of chaos. This thesis will explore the use of analog op amp circuits to model the Ueda oscillator, a simplification of the Duffing oscillator, and will compare it with a digital simulation. The thesis starts with an investigation of the basic piece of phase space flow computation, the integrator. Next is an investigation of simple linear differential equation/circuit, and lastly the Ueda equation/circuit is modeled. The results of the analog simulation are qualitatively compared with a digital simulation. It is found that the analog computer models the equation well for higher driving frequencies (> 0.5 Hz). The phase space flows of the two simulations are similar in this range.