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
Email: sprott@juno.physics.wisc.edu
Home Page: https://sprott.physics.wisc.edu/