WOLFRAM|DEMONSTRATIONS PROJECT

Three-Dimensional Linear System of DEs

​
time
100
polynomial parameters
h shift
-0.2
v shift
0
skew
-1
initial conditions
x
0
-1.8
y
0
1.8
z
0
1.8
eigenvalues: -0.20-1.00, -0.20+1.00, -0.20
The dynamics of a system of three differential equations may be analyzed using the eigenvalues of the coefficient matrix. For example, the origin will be attractive if the real parts of all eigenvalues are negative and the system will be rotational if there are complex eigenvalues. The eigenvalues are determined by the roots of the characteristic polynomial, whose graph is shown at the right.