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REALFP

As a very simple test case we define a dynamical system, which has exactly one critical point at the origin of phase space and real eigenvalues/-vectors of the Jacobian matrix there:

$\displaystyle \dot{x}$	=	$\displaystyle A\cdot{}x,\quad{}A\ne{}0$
$\displaystyle \dot{y}$	=	$\displaystyle B\cdot{}y,\quad{}B\ne{}0$
$\displaystyle \dot{z}$	=	$\displaystyle C\cdot{}z,\quad{}C\ne{}0,\ A\ge{}B\ge{}C$

Depending on the values of A, B, and C the critical point is either attracting, repelling, or a saddle critical point. Note, that relation $A\ge{}B\ge{}C$ is not a restriction to this system, since axes x, y, and z are arbitrary choices and can be reordered to fulfill any other relation between A, B, and C.

$\displaystyle 0>A\ge{}B\ge{}C$	$\textstyle \to$	attracting node
$\displaystyle A>0>B\ge{}C$	$\textstyle \to$	saddle node (attracting x axis)
$\displaystyle A\ge{}B>0>C$	$\textstyle \to$	saddle node (repelling z axis)
$\displaystyle A\ge{}B\ge{}C>0$	$\textstyle \to$	repelling node

Next: COMPLFP Up: Sample dynamical systems Previous: Sample dynamical systems

Helwig Löffelmann, November 1998,

mailto:helwig@cg.tuwien.ac.at.