🚀 go-pugleaf

From article <93024.164511WAJ@psuvm.psu.edu>, by WAJ@psuvm.psu.edu:
> I have recently begun experimenting with modelling of chaotic systems in
> C++. The only system I have had success with is the Lorenz water wheel
> (as found in James Gleick's Chaos). Does anybody know of any other fairly
> simple physical systems which exhibit chaotic behavior?
> (btw, if anybody wants to see the wheel, i could send it)
> thanks
> 
> Bill Jester

Indeed!  Try a duffing oscillator ( a nonlinear spring - mass system)

Here it is in coupled first order form (I assume you are using some
numerical ODE integrator such as a Runge-Kutta algorithm)

dx(1)/dt = x(2)

dx(2)/dt = -k*x(2) -a*x(1) -b*[x(1)]^3 + F*cos(w*t)

k is the damping parameter, F is the forcing amplitude, w is the forcing 
frequency, a and b are the spring parameters

A period-doubling sequence may ba observed with the parameters:

a=0
b=1
k=0.1
w=1
with initial conditions x(1) = 1, x(2) = 1
let F range from 9.8 to 10

These parameters were studied by Ueda

Phase plots are interesting for the period doubling sequence, but 
a first return map is far more useful for the complex regions.

Have Fun,

-Ken Hamer