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Topic: Simple Difference Equation problem
Replies: 2   Last Post: Jul 17, 2014 9:37 PM

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Ken.Pledger@vuw.ac.nz

Posts: 1,380
Registered: 12/3/04
Re: Simple Difference Equation problem
Posted: Jul 17, 2014 8:03 PM
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In article <7d74bcc5-412e-4905-8906-510c9061c0aa@googlegroups.com>,
gyansorova@gmail.com wrote:

> Consider a simple scalar non-linear difference equation
>
> x(n+1)=x(n)-mu.x(n)^2+ mu.u
>
> where u is a positive constant input (say unity or whatever) and mu is
> selected for stability.
>
> The equilibrium point is when x(n+1)=x(n) giving
>
> x*=sqrt(u) - take positive root only here and assume mu>0.
>
> Linearise and we get
>
> x(n+1)=a.x(n)+mu.u
>
> where a=1-2.mu.sqrt(u)



I'm no expert at this, but why is that 2 there? Could it be that

a = 1 - mu.sqrt(u) ?

Ken Pledger.



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