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Unformatted text preview: ˆ x to the system of nonlinear ordinary differential equations d x dt = fx is of the following type if the eigenvalues of the Jacobian J ˆ x 1 , ˆ x 2 ( ) matrix J have the following properties: i) Both are real and negative ⇒ ˆ x is a stable node ii) Both are real and positive ⇒ ˆ x is an unstable node iii) Both are real, with one negative and one positive ⇒ ˆ x is an unstable node iv) They are complex conjugative with negative real parts ⇒ ˆ x is an stable center (spiral) v) They are complex conjugative with positive real parts ⇒ ˆ x is an stable center (spiral)...
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- Fall '10
- Chaos Theory, Complex number, Fundamental physics concepts