What is the 'stability' of a critical point of a ( 1 dimensional) dynamical system?

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College
Calculus and Analysis
Differential Calculus
Critical Point

MMDCCC50m

Answered question

2022-11-11

What is the 'stability' of a critical point of a (

1

dimensional) dynamical system?

Answer & Explanation

h2a2l1i2morz

Beginner2022-11-12Added 19 answers

Stability means that for any sufficiently close initial condition to your equilibrium point (better than "critical point"), the corresponding solution will stay close to the equilibrium point for all positive times.
For example, this happens with the equilibrium point

0

of the equation

x^{'} = 0

. In particular, this shows that there is no need to have nonzero signs for the derivative above and below the equilibrium point.

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