'Lyapunov' diaporamas de présentation

time (t)

Analyze the non-autonomous systems by adapting (extending) the tools we developed for autonomous systems. Response not affected by t 0. Autonomous vs. Nonautonomous. x(t) versus time (t). t 0 =0. t 0 =3. t 0 =6. t 0 =9. x(t 0 )=3. x(t). Response depends on t 0. x(t) versus time (t).

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Lyapunov and diffusion timescales in the Solar system 1. Separatrix maps and chaotic layers

Lyapunov and diffusion timescales in the Solar system 1. Separatrix maps and chaotic layers. I. I. Shevchenko Pulkovo Observatory. Abstract.

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Lyapunov Exponents

Lyapunov Exponents. By Anna Rapoport. Lyapunov A. M. (1857-1918). Alexander Lyapunov was born 6 June 1857 in Yaroslavl, Russia in the family of the famous astronomer M.V. Lypunov, who played a great role in the education of Alexander and Sergey.

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Modal Dynamics of Wind Turbines with Anisotropic Rotors Peter F. Skjoldan 7 January 2009

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Lecture 07 Analysis (III) -- Stability

Lecture 07 Analysis (III) -- Stability. 7.1 Bounded-Input Bounded-Output (BIBO) Stability 7.2 Asymptotic Stability 7.3 Lyapunov Stability 7.4 L inear Approximation of a Nonlinear System. Bounded-Input Bounded-Output (BIBO) stablility. Definition: For any constant N , M >0.

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EXAMPLES:

EXAMPLES:. Example 1: Consider the system. Calculate the equilibrium points for the system. Plot the phase portrait of the system. Solution:. The equilibrium points must be stationary. Therefore for the first system we have. roots([-1/16 0 0 0 1]) ans = -2.0000

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EXAMPLES:

EXAMPLES:. Example 1: Consider the system. Calculate the equilibrium points for the system. Plot the phase portrait of the system. Solution:. The equilibrium points must be stationary. Therefore for the first system we have. roots([-1/16 0 0 0 1]) ans = -2.0000

324 views • 16 slides