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Math Help - Stable, but not asymptotically stable

  1. #1
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    Stable, but not asymptotically stable

    Hi everyone.

    My task from difference equations is:

    Lets suppose we have a nonlinear dynamic system x(t+1) = f(x(t)) , the status space X from R (real) and a fixed point xHAT.
    Find a function f from C1 and a set X from R (real) , so that f ' (xHAT) = 1 and xHAT is stable, but NOT ASYMPTOTICALLY stable fixed point of our system.

    Any suggestions?

    Thx,
    Naena
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Naena View Post
    Hi everyone.

    My task from difference equations is:

    Lets suppose we have a nonlinear dynamic system x(t+1) = f(x(t)) , the status space X from R (real) and a fixed point xHAT.
    Find a function f from C1 and a set X from R (real) , so that f ' (xHAT) = 1 and xHAT is stable, but NOT ASYMPTOTICALLY stable fixed point of our system.

    Any suggestions?

    Thx,
    Naena
    Look at f(x)= x- 1.
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  3. #3
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    and a fixed point?
    I doubt its correct, cause the task is not only to find a function with f ' = 1 in fixet point xHAT, but it also has to have a stable fixed point xHAT, which means xHAT=f(xHAT).
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