Unformatted text preview: ) For any u let g ( u,t ) be the solution satisfying g ( u, 0) = u . (i) A point u * is Lyapunov stable if and only if for all ± > 0 there exists δ > 0 such that if | u *-v | < δ then | g ( u * ,t )-g ( v,t ) | < ± for all t ≥ 0. (ii) A point u * is quasi-asymptotically stable if and only if there exists δ > 0 such that if | u *-v | < δ then | g ( u * ,t )-g ( v,t ) | → 0 as t → ∞ . (iii) A point u * is asymptotically stable if and only if it is both Lyapunov stable and quasi-asymptotically stable....
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This note was uploaded on 10/19/2011 for the course MATH 3354 taught by Professor Drager during the Fall '08 term at Texas Tech.
- Fall '08