CDS - Examples of Nullclines

Remember:

• Saddle:
  
• Stable Spiral:
  
• Center:
  
• Lines of Steady States:
  

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• The nullclines are in this case:
  • $y=-4x$
  • $y=2x$
  • And are represented in the phase space as the black lines.
• The blue arrows are found via a simulation.
• This should be an attractive ssnot-sure-about-this

• The $(0,0)$ point this time is an unstable ss.

• asymptotically stable ss
• Negative eigenvalues, we will see more in detail later

• Lyapunov stable ss
• Immaginary eigenvalues, we will see more in detail later

• marginally stable ss