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i have a higher order system with a single fixed point. i chose such parameters that the fixed point is unstable. so it should either oscillate to infinity, or in this case it actually has a limit cycle. when running this system on the computer, it does get to that limit cycle for most initial conditions, i.e. max amplitude of 23.8 and and min at .8 while the steady state is at 3.9. but the problem is that if i choose all of the initial conditions to the same value, then instead of the limit cycle it just converges to that single value of 3.9. The other problem is that when i pick initial conditions close to that 3.9 steady state, it actually takes a very long time to converge to the limit cycle(it takes more periods than if i had taken some random values not even close to the limit cycle values), while i want it to converge to the limit cycle very quickly.

And what i'd like to know is if there are ways to get to a limit cycle very quickly!? Because i'm trying to think of a strategy of what system would be more resistant to oscillations. I figure if limit cycles take your initial conditions all over the places, then it's no good, and i'll have more correlation with just a regular stable spiral.

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# Help-higher order limit cycles

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