ABSTRACT

Systems of differential equations can be solved not only algebraically and numerically (i.e. by usage of digital computers), but also by simulation with analog devices as transistors, capacitors, resistors, diodes, linear amplifiers.

This method is applied to the Lorenz equations, the famous systems of nonlinear differential equations exhibiting chaos.

Measurements are done with a Hybrid system consisting of an analog computer and a digital data-acquisition system.

This work gives a general introduction into the Lorenz system and observes the behaviour of its solutions for different Bifurcation parameters.

Title Page, Signature Page, Original Abstract Page, Original Table of Contents Page, Acknowledgments

Introduction 1, 2

The Lorenz Equations 3, 4, 5, 6, 7, 8

Lyapunov Exponents 9, 10, 11

Apparatus 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Results 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47

Conclusion 48, 49, 50

Applications 51

Future Work 52, 53, 54, 55

Programs in ASYST 56, 57, 58, 59, 60, 61

Picture Album of the Lorenz Attractor 62, 63, 64, 65, 66, 67

Surface of Fourier Plots 68, 69

3d Animation of the Lorenz Attractor 70, 71, 72, 73

References 74, 75, 76, 77

Vita 78