Consider the system dx dt = ax ( 1 ? y 2 ) , dy dt = by
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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 tha
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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. (a) Let a = 1 and b = 1. Plot the trajectory in the phase plane and determine (or estimate) the period of the oscillation. (b) Repeat part (a) for a = 3 and a = 1 3 , with b = 1. (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.
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