Consider the system dx dt = ax_1 y 2 _, dy dt = by_1 + x 3 _, where a and b are positive

Chapter 9, Problem 9

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Consider the system dx dt = ax_1 y 2 _, dy dt = by_1 + x 3 _, where a and b are positive constants. Observe that this system is the same as in the example in the text if a = 1 and b = 0.75. Suppose the initial conditions are x(0) = 5 and y(0) = 2. G a. Let a = 1 and b = 1. Plot the trajectory in the phase plane, and determine (or estimate) the period of the oscillation. G b. Repeat part a for a = 3 and a = 1/3, with b = 1. G c. Repeat part a for b = 3 and b = 1/3, with a = 1. d. Describe how the period and the shape of the trajectory depend on a and b. 1