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Do the following flows define continuous-time dynamical systems? Prove your statement and, if they are dynamical systems then sketch their behaviour in the phase space and the extended phase space. (a) X = R, T = Rj. Stx := x + 2t (b) X = R, T = R†. S;x := 2x + t (c) X = R, T = Rj. S¿x := xe'

Do the following flows define continuous-time dynamical systems? Prove your statement and, if they are dynamical systems then sketch their behaviour in the phase space and the extended phase space. (a) X = R, T = Rj. Stx := x + 2t (b) X = R, T = R†. S;x := 2x + t (c) X = R, T = Rj. S¿x := xe'

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Do the following flows define continuous-time dynamical systems? Prove your statement and, if they are dynamical systems then sketch their behaviour in the phase space and the extended phase space. (a) X = R, T = R†. S;x := x + 2t (b) X = R, T = R*. S;x := 2x + t (c) X = R, T = Rj. S̟x := xe'
Transcribed Image Text:Do the following flows define continuous-time dynamical systems? Prove your statement and, if they are dynamical systems then sketch their behaviour in the phase space and the extended phase space. (a) X = R, T = R†. S;x := x + 2t (b) X = R, T = R*. S;x := 2x + t (c) X = R, T = Rj. S̟x := xe'
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