- Consider The System X Y Y X Dy With Non Negative Parameter 8 A Show That When D 0 The System Is Hamiltonia 1 (31.41 KiB) Viewed 304 times
Consider the system x = y, y = -x³ - dy with non-negative parameter 8. (a) Show that when d = 0 the system is Hamiltonia
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Consider the system x = y, y = -x³ - dy with non-negative parameter 8. (a) Show that when d = 0 the system is Hamiltonia
Consider the system x = y, y = -x³ - dy with non-negative parameter 8. (a) Show that when d = 0 the system is Hamiltonian. (b) Show that when d = 0 solutions near the origin are periodic. (c) Find a Lyapunov function and show that the origin is a stable fixed point. (d) For this last part consider x = y, y=-x³ + x-dy. Assume that 0 < 5 <√8. Find the nullclines, classify the fixed points, and sketch the phase portrait.