Simple Chaotic Systems and Circuits

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Table of Contents

Simple Chaotic Systems and Circuits

Acknowledgments

Outline

Abbreviated History

Mathematical Models of Dynamical Systems

Poincaré-Bendixson Theorem (in 2-D flow)

Autonomous Systems

Lorenz Equations (1963)

Rössler Equations (1976)

Lorenz Quote (1993)

Rössler Toroidal Model (1979)

Sprott (1994)

Gottlieb (1996)

Sprott (1997)

Bifurcation Diagram

Return Map

Fu and Heidel (1997)

Weaker Nonlinearity

Regions of Chaos

Linz and Sprott (1999)

General Form

Operational Amplifiers

First Circuit

Bifurcation Diagram for First Circuit

Computer Prediction for First Circuit

Second Circuit

Chaos Circuit

Third Circuit

Chua’s Circuit (1984)

Chaotic Inductor-Diode Circuit Testa, Perez, & Jeffries (1982)

References

Author: J. C. Sprott

Email: sprott@juno.physics.wisc.edu

Home Page: http://sprott.physics.wisc.edu/