Re: Chaos Prediction?

From: Krunom Ilicevic (krunom_at_hotmail.com)
Date: 09/24/04 

Date: Fri, 24 Sep 2004 08:54:24 +0200

> If you have your dynamical system in the form of an exact differential
> equation, you are already a lucky man.
> Then you can use numerical simulation.

Thanks for answer...
Physical dynamical system is non-autonomous (excitation is E*sin(t)) and the
rest of diff. equation is describing "passive" part of ph. dyn. system:

x''+ax'+bx+f(x)

 and this part is the same (it should be?) for all amplitudes of excitation
(for all bifurcation-parameters) -00<E<+00, only E changes. And because of
that i must not estimate "passive part" of equation for different E's. Yes,
im lucky man ; )

> It is no problem to set E=2.5 numerically.

And here is the problem:
I CAN numerically solve problem for E=2.5, but i DONT WANT it. I know, im
weird... : - o
I want to solve diff. equation ONLY for, an example, 0<E<1 and from this
results i want to predict:

"For E>1 pitchfork bifurkation will appear!"

or something similar (histeresys, perioddoubling...). At the moment it isnt
neccessary to say precise:

"For E=2.1 pitchfork bif. appears!"

i only want to predict some phenomena for bif. parameter interval that isnt
"analysed":

"I analyzed for 0<E<1 and from these results I can say (more or less
precise) what would/will happen for E>1"

Is there a way to predict phenomena in this way?

Thanks.