Helper Codes and Model Parameters

Codes

1. The Runge-Kutta 4th order modular ODE solver for the mass on a spring problem
   
   
2. Initial conditions generator code, HO_setup.c or HO_setup.cpp , to display Harmonic Oscillator and one-well modified phase space
   
   
3. Initial conditions generator code, 2w_setup.c or 2w_setup.cpp , to display phase space of two-well potential phase space
   
   
4. Initial conditions generator code, 2w_setup_homclinic.c or 2w_setup_homclinic.cpp , to display homoclinic orbit in two-well potential
   
   
5. Initial conditions generator code, 2w_setup_chaotic_attractor.c or 2w_setup_chaotic_attractor.cpp , to display the chaotic attractor in a dissipative driven two-well potential
   
   
6. Stroboscopic analysis code, stroboscopic.c or stroboscopic.cpp , to display the chaotic attractor in a dissipative driven one- or two-well potential. It assumes omega = 1.0
   
   

ODE solver code: duffing.c or duffing.cpp

Model Parameters

The following are suggested parameters that lead to interesting results.

One-well Duffing Oscillator:

Parameters: $\alpha = 1.0$, $\beta = 1.0$, $\mu = 0.1$, $\omega = 1.0$ and $A$ in the range [2.0, 35.5]

Two-well Duffing Oscillator

Parameters: $\alpha = 1.0$, $\beta = -1.0$, $\mu = 0.25$, $\omega = 1.0$ and $A$ with values [0.22, 0.245, 0.4]