General 2D Dynamical Systems with application to van der Pol dynamics (9.7.2010)

General System Trajectories

General trajectory analysis module

Dynamical 2D System Trajectories: Steven H. Strogatz Nonlinear dynamics and Chaos, Westview Pess, 1994 Example7.6.3 two-timing (two time scale) analysis of the van der Pol oscillator (with comparison of a growth envelope functin with a Verhulst logistic growth function)

For DS of the form x'=ax+by, y'=cx+dy, the (only) fixed point is at the origin {0,0}.

van der Pol trajectory and growth equations

Estimate the relation between the van der Pol damping parameter and the logistic growth rate by expanding the envelope functions and comparing lowest order terms

Compare behavior of van der Pol and logistic envelope functions (for typical parameter values)

Stragatz Example7.6.3

van der Pol oscillator with larger damping parameter μ