The limit cycle found in Problem 2 comes into existence as a result of a Hopf bifurcation at a value
a) Draw plots of trajectories for different values of
b) Calculate eigenvalues at critical points for different values of
c) Use the result of Problem 3(b) in Section 7.6.
(a) By solving Eq. (9) numerically, show that the real part of complex root changes sign
when
(b) show that a cubic polynomial
(c) By applying the result of part (b) to Eq. (9) show that the real part of the complex root changes sign when
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Differential Equations: An Introduction to Modern Methods and Applications
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