# Thread: Several concepts in Dynamic System

1. ## Several concepts in Dynamic System

I have several questions regarding some concepts of dynamic system.
1. A dynamic system is hyperbolic if all of the eigenvalue of Df(a) have non-zero real point
Does it mean that the DS(dynamic system) is hyperbolic when the eigenvalue is strictly non-zero and real? or is it also hyperbolic if the real parts of eigenvalues are non zero. when the eigenvelues includes some imaginary parts and real parts?
2. Stability of equilibrium points.
I found equilibrium points and processed it through jacobian matrix, so I have found some eigenvalues of jacobian matrix for each equilibrium points. now I want to state the stability of equilibrium points but I do not know how to determine if it is stable or unstable or center manifold. How can I find out the stability?

2. ## Re: Several concepts in Dynamic System

I kninda found out by myself for second question.

3. ## Re: Several concepts in Dynamic System

Originally Posted by delune23
I have several questions regarding some concepts of dynamic system.
1. A dynamic system is hyperbolic if all of the eigenvalue of Df(a) have non-zero real point
Does it mean that the DS(dynamic system) is hyperbolic when the eigenvalue is strictly non-zero and real? or is it also hyperbolic if the real parts of eigenvalues are non zero. when the eigenvelues includes some imaginary parts and real parts?
You said, above, that a system is hyperbolic if all of its eigenvalues have non-zero real part. That would include, but not be restricted to, eigenvalues that have non-zero real part but zero imaginary part- i.e. real numbers.

2. Stability of equilibrium points.
I found equilibrium points and processed it through jacobian matrix, so I have found some eigenvalues of jacobian matrix for each equilibrium points. now I want to state the stability of equilibrium points but I do not know how to determine if it is stable or unstable or center manifold. How can I find out the stability?
An equilibrium point is stable if all of its eigenvalues havenon-positive (negative or 0) real part.