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Limit Cycle

by Nusc
Tags: cycle, limit
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Nusc
#1
Mar27-10, 10:44 PM
P: 780
http://books.google.ca/books?id=Pd8-...ed=0CAkQ6AEwAA


Let ~ denote vector.
For a fixed point.
(~x0 is asymptotically stable if there exists
a neighbourhood U of ~x0 such that if ~x(t) obeys Hamilton's equations and ~x(0) in U, then lim
t->inf
~x(t) = ~x0.)

can you give me a precise definition for periodic solutions (limit cycles) in this context?
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Eynstone
#2
Apr9-10, 06:42 AM
P: 336
Quote Quote by Nusc View Post
http://books.google.ca/books?id=Pd8-...ed=0CAkQ6AEwAA


Let ~ denote vector.
For a fixed point.
(~x0 is asymptotically stable if there exists
a neighbourhood U of ~x0 such that if ~x(t) obeys Hamilton's equations and ~x(0) in U, then lim
t->inf
~x(t) = ~x0.)

can you give me a precise definition for periodic solutions (limit cycles) in this context?
A solution x is periodic iff there exists T >0 with x(t+T) = x(t) for all t.


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