Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

for a Van Der Pol dyanmical sysetm , governed by the eqautions

x' = a * (x - 0.3 x ^3 ) - y

y' = x

i read at http://www.scholarpedia.org/article/Van_der_Pol_oscillator that when the system is away from the curve y=x−x3/3 , "a relation |x˙| >> |y˙|=O(1/ϵ) is obtained from equations (2) and (3). Therefore, the system moves quickly in the horizontal direction. When the system enters the region where |x−x3/3−y|=O(1/ϵ2) , x˙ and y˙ are comparable because both of them are O(1/ϵ)".

I really do not get this entirely.`I am unsure of how the relationship involving the infinitesimals are derived. How are these realtionship justified?

Can anybody please try to give us a hint? Thank you so much

Muzialis

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Van Der Pol dynamics

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**