Stability Matrix
المؤلف:
Tabor, M
المصدر:
"Linear Stability Analysis." §1.4 in Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley
الجزء والصفحة:
...
5-7-2018
955
Stability Matrix
Given a system of two ordinary differential equations
let 
and 
denote fixed points with 
, so
Then expand about 
so
To first-order, this gives
![d/(dt)[deltax; deltay]=[f_x(x_0,y_0) f_y(x_0,y_0); g_x(x_0,y_0) g_y(x_0,y_0)][deltax; deltay],](http://mathworld.wolfram.com/images/equations/StabilityMatrix/NumberedEquation1.gif) |
(7)
|
where the 
matrix, or its generalization to higher dimension, is called the stability matrix. Analysis of the eigenvalues (and eigenvectors) of the stability matrix characterizes the type of fixed point.
REFERENCES:
Tabor, M. "Linear Stability Analysis." §1.4 in Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, pp. 20-31, 1989.
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