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Unformatted text preview: of the equilibrium at the origin of the Lorentz system x = x + yz, y = y + z, z = yx + y z, where , are positive parameters and = 1. Estimate the rate of convergence of x ( t ) , y ( t ) , z ( t ) to zero. Problem 5.4 Check local asymptotic stability of the periodic trajectory y ( t ) = sin( t ) of system y ( t ) + y ( t ) + y 3 = sin( t ) + cos( t ) + sin 3 ( t ) . Problem 5.5 Find all values of parameter a R such that every solution x : [0 , ) R 2 of the ODE cos(2 t ) a x ( t ) = cos 4 ( t ) sin 4 ( t ) x ( t ) converges to zero as t when > is a suciently small constant....
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 Spring '09
 AlexandreMegretski
 Dynamics

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