Unformatted text preview: , 0) of the following system is asymptotically stable: ˙ x = 2 y 3-x 5 , ˙ y =-x-y 3 + y 5 . [Hint: construct a suitable Lyapunov function of the form ax 2 + y 4 ] IV. Periodic orbits Problem 36.1 [Also, give an argument based on the dissipation of energy] (X4) Draw the phase portrait for the (Rayleigh) equation ¨ x + μ ( ˙ x 3-˙ x ) + x = 0 with μ = 1 and μ = . 1. Show the limit cycles. 1...
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- Spring '10
- phase portrait, Stability theory, III. Lyapunov functions, suitable Lyapunov function, II. Dissipative systems, I. Conservative systems