Dynamical systems

• How to Write Coupled Nonlinear ODEs in State-Space Form
  Convert coupled nonlinear ODEs to first-order state-space form by choosing state variables, solving for their derivatives, and defining outputs.
• Can You Prove Sensitivity to Initial Conditions Numerically?
  Numerical simulations can provide evidence of sensitivity to initial conditions, but a plot alone is not a proof. Here is a reliable test using the Lorenz system.
• What Quantity Is Conserved in the Lotka–Volterra System?
  For the standard Lotka–Volterra predator–prey equations, a conserved quantity is d x − c ln x + b y − a ln y; here is its derivation.
• How to Use Variation of Parameters for a 3×3 System
  Use a fundamental matrix to solve a nonhomogeneous 3×3 linear ODE system by variation of parameters, with a worked example.