1D Dynamical systems

Learning objectives

  • Define (autonomous) dynamical system
  • Put nonautonomous or second order DEs into (autonomous) dynamical system form
  • Display a 1D dynamical system, dx/dt = f(x) on the (dx/dt vs x)-plane and perform a state line analysis
  • Find equilibrium (aka constant) solutions and determine their stability
  • Do a linear stability analysis to describe the behavior of solutions near an equilibrium
  • Give a potential function interpretation of 1D dynamical systems

Before class

  • Read Borrelli-Coleman section 2.8
  • Read notes

In class