WOLFRAM|DEMONSTRATIONS PROJECT

Linear ODE Forms

matrix M

nodal source

The fixed point

(0,0)

has many different stability types. A system rarely has an infinite number of solutions along a line in the

x(t)

,

y(t)

plane.

The fixed point

(0,0)

has many different stability types. Only two solutions for fixed points are possible in a linear first-order system: one with an equilibrium point at

(0,0)

, or infinitely many solutions along a line in the

x(t)

,

y(t)

plane.

Red dots represent fixed points or equilibrium points.

Dashed blue lines indicate straight-line solutions.

Dashed black lines indicate nullclines.