(a) For the system dx dt = x + x3, dy dt = y sketch phase portraits...

(a) For the system dx dt = μx + x3, dy dt = −y sketch phase portraits forμ < 0, μ = 0, andμ > 0. Plot a bifurcation diagram.

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(b) Plot a phase portrait and Poincaré section for the forced Duffing system dx dt = y, dy dt = x − 0.3y − x3 + 0.39 cos(1.25t).

Describe the behavior of the system.

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426 18. Examination-Type Questions