
Interpretation:
All the qualitatively different
Concept Introduction:
The qualitative change in the dynamics of the flow with parameters is called bifurcation and the points at which this occurs is called bifurcation points.
The stability of the dynamical systems is tudied using bifurcation.
Transcritical bifurcation is one of the bifurcation mechanism in which two fixed points exchange their stability instead of destroying.
In the transcritical bifurcation, fixed points exist for all values of the parameter.

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Chapter 3 Solutions
Nonlinear Dynamics and Chaos
- Q/ show that H (X,Y) = x²-4x-x² is 2 first integral of the system Y° = y 0 y° = 2x + x 3 then study the stability of critical point and draw phase portrait.arrow_forwardQ/Given the function H (X,Y) = H (X,Y) = y 2 X2 2 2 ²** 3 as a first integral, find the correspoding for this function and draw the phase portrait-arrow_forwardQ/ show that the system has alimit cycle and draw phase portrait x = y + x ( 2-x²-y²)/(x² + y²) ½ 2 y = -x+y ( 2-x² - y²) / (x² + y²) ½/2arrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage