e) Consider the flow ϕt (v) = e^(tA) v, v in R^(n) generated by the linear system x' = Ax where A in M (n, R). e1) Give a condition that implies that o bar is a Poincare stable fixed point for the above flow. e2) Is this condition a necessary conditon? e3) Give a condition that implies that o bar is a Lyapunov stable fixed point for the above system. e4) Is this condition necessary?
e) Consider the flow ϕt (v) = e^(tA) v, v in R^(n) generated by the linear system x' = Ax where A in M (n, R). e1) Give a condition that implies that o bar is a Poincare stable fixed point for the above flow. e2) Is this condition a necessary conditon? e3) Give a condition that implies that o bar is a Lyapunov stable fixed point for the above system. e4) Is this condition necessary?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
e) Consider the flow ϕt (v) = e^(tA) v, v in R^(n) generated by the linear system x' = Ax where A in M (n, R). e1) Give a condition that implies that o bar is a Poincare stable fixed point for the above flow. e2) Is this condition a necessary conditon? e3) Give a condition that implies that o bar is a Lyapunov stable fixed point for the above system. e4) Is this condition necessary?
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