Critical point analysis for x′=y,y′=x2−y−epsilon

bucstar11n0h 2022-11-21 Answered
Critical point analysis for x = y , y = x 2 y ϵ
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Tasinazzokbc
Answered 2022-11-22 Author has 17 answers
There is a theorem which says so long as the critical (or equilibrium) point is not a center then the nature of this critical point in the system There is a theorem which says so long as the critical (or equilibrium) point is not a center then the nature of this critical point in the system x′,y′, is the same as that point in the linearization i.e,, is the same as that point in the linearization i.e,
x ~ = p x ( x 0 , y 0 ) x + p y ( x 0 , y 0 ) y
y ~ = q x ( x 0 , y 0 ) x + q y ( x 0 , y 0 ) y
where x = p ( x , y ) and y = q ( x , y ). Now you have a linear system. Find the associated matrix to this system, compute it's eigenvalues and use the Painleve Analysis.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more