Introduction to Applied Nonlinear Dynamical Systems and Chao

Introduction to Applied Nonlinear Dynamical Systems and Chaos , 2nd addition

Consider the planar system (a) Convert the system to polar coordinates. (b) how that there are limit cycles near Al 0 for u 0, and there is no limit cycle for Au S 0. (c) Plot the three-dimensional bifurcation diagram in r, y, Au space, with directions of the flow for different Au values. (d) Plot the phase portrait for Au 0, and determine the stability of these limit cycles. (Hint: Checking the behaviors of the orbits following their radius in polar coordinates can help you. (e) Plot the phase portrait for Au 0, and determine the stability of these fixed points. (Hint: Checking the behaviors of the orbits following their radius in polar coordinates can help you.

Solution