Examples of Phase Plane Diagrams

  • Center: dx/dt = y, dy/dt = - x

  • Saddle: dx/dt = y, dy/dt = x

  • Stable Spiral: dx/dt = y, dy/dt = - x - y

  • Unstable Spiral: dx/dt = y, dy/dt = - x + y

  • Saddle and Unstable Spiral: dx/dt = x - y, dy/dt = 1 - x y

  • Limit Cycles: dx/dt = y + x sin(Pi r)/r, dy/dt = -x + y sin(Pi r)/r