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CHAOS Strange Attractors and Lorenz Equations
Definitions ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Definitions & Applications of Attractors
Applications of Attractors Chua   Duffing   Lorenz R össler   Ikeda
Edward Lorenz ,[object Object],[object Object],[object Object]
[object Object],Lorenz Attractor
[object Object],The Lorenzian Waterwheel
Lorenz Equations
The Variables ,[object Object],[object Object],[object Object]
The Constants ,[object Object],[object Object],[object Object]
Behavior ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Butterfly Effect ^ x solution with respect to time. ^ y solution with respect to time. «  z solution with respect to time.
Proof for Bounded System ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proof Cont. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proof Cont. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Proof Finale ,[object Object],[object Object],[object Object]
The End

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