Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I heard that a system of nonlinear equations is unstable.

I am curious of how "instability" is defined, and why do nonlinear equations show instability?

Edit: OK, so what about contexts in matrices -> when one says a matrix $A$ is unstable? eg. $x(t+1) =Ax(t)$? What instability is it talking about?

share|improve this question
Please see the update I made to my response using Wikipedia. Have fun! -A –  Amzoti Dec 6 '12 at 6:29
add comment

1 Answer 1

up vote 2 down vote accepted

I think you need to be more specific regarding what you mean by instability because you have to choose that for Lyapunov, orbital, structural and input-output stability. There are also many kinds/classes of nonlinear equations that these can apply to.

Review these nice survey papers of stability and you'll see what is meant by instability based on the type of stability you are talking about. Additionally, see the bibliographies for books and other papers:

http://www.me.berkeley.edu/ME237/7_stability.pdf, and

http://www.ee.cityu.edu.hk/~gchen/pdf/C-Encyclopedia04.pdf .

Lastly, see the section titled "Stability of fixed points" at http://en.wikipedia.org/wiki/Stability_theory for stability statements that couple eigenvalues to a statement about the different ways to look at stability.

There are many wonderful books dedicated to this subject.

Is this what you were looking for or book references too?

Regards -A

share|improve this answer
Great job, again!! +1 –  amWhy May 16 '13 at 0:59
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.