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Lyapunov Exponent

Lyapunov Exponent. Eui-Sun Lee Department of Physics Kangwon National University. Measure of The degree of Sensitivity on The Initial Conditions. Chaotic Orbit given Initial Condition Periodic Orbit given Initial Condition.

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Lyapunov Exponent

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  1. Lyapunov Exponent • Eui-Sun Lee • Department of Physics • Kangwon National University Measure of The degree of Sensitivity on The Initial Conditions. Chaotic Orbit given Initial Condition Periodic Orbit given Initial Condition

  2. Lyapunov Exponent( σ) • Perturbation : • Let be the separation after t-th ● ● iteration. ● ● ● ● is called the Lyapunov exponent . then If

  3. Determination of Sensitivity On the initial condition For the case of Period-q Orbit, the Stability Multiplier is Hence, The Lyapunove Exponent Becomes for the Period-q Orbit. • > 0 : Exponential divergence , Chaotic Attractor. • Sensitive on the initial condition • < 0 : Exponential convergence , Regular Periodic attractor. • Non-sensitive on the initial condition

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