(a) Show that there are no critical points when c < ? 0.
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(a) Show that there are no critical points when c < ? 0.5, one critical point for c = ? 0.5, and two critical points whe
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(a) Show that there are no critical points when c < ? 0.5, one critical point for c = ? 0.5, and two critical points when c > ? 0.5. (b) Find the critical point(s) and determine the eigenvalues of the associated Jacobian matrix when c = ? 0.5 and when c = 1. (c) How do you think trajectories of the system will behave for c = 1? Plot the trajectory starting at the origin. Does it behave the way that you expected? (d) Choose one or two other initial points and plot the corresponding trajectories. Do these plots agree with your expectations?
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