So I've been working to achieve chaos from a damped pendulum. The acceleration equation for a damped simple pendulum that I'm using is:

$\displaystyle a= -cv + bx - dx^3 + F\cos{\omega t}$


  • -cv is the Restoring Force
  • bx-dx^3 is the Duffing Oscillator
  • F cos(...) is the Driving force

I have implemented the above equation in C++, and using runge kutta I have been able to plot a phase portrait graphs of v vs x. Both simple and damped conditions have been verified, but I'm am currently having problems searching for the correct initial conditions that would lead the above equation to chaos.

Any pointers?