# 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