Register to reply

Van Der Pol dynamics

by muzialis
Tags: dynamics
Share this thread:
muzialis
#1
Dec5-11, 05:54 AM
P: 152
Hi All,

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/...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
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history

Register to reply

Related Discussions
Time taken for a car to stop Calculus & Beyond Homework 1
Dynamics of a spring contrained string over a pulley. Engineering, Comp Sci, & Technology Homework 2
Dynamics - vertical spring and horizontal pendulum problem General Engineering 0
Dynamics and action-reaction pairs Classical Physics 11
Molecular Dynamics vs Rigid Body Dynamics General Physics 4