4. Use Liapunov's function V(x) = x² + x² + x² to prove that the origin is an asymptotically stable equilibrium of the system .18 || = −x₂ − x₁x² + x² – x³ x₁ + x²-x² _—X1X3 — X3x² — x2x² – x²

4. Use Liapunov's function V(x) = x² + x² + x² to prove that the origin is an asymptotically stable equilibrium of the system .18 || = −x₂ − x₁x² + x² – x³ x₁ + x²-x² _—X1X3 — X3x² — x2x² – x²

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.5: Nonlinear Systems Of Differential Equations

Problem 11E: Whales and Krill For the system of differential equations 10, suppose that F11 and F21. Show that...

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Question

4. Use Liapunov's function V(x) = x² + x² + x² to prove that the origin is
an asymptotically stable equilibrium of the system
.18
||
−x₂ − x₁x² + x² – x³
x₁ + x²-x²
-X1X3 — X3x² − x2x² – x²]

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