Interpretation:
For the system
All the bifurcations that occur as
Concept Introduction:
Fixed points are the points where
The graph of the vector field for different values of
The saddle-node bifurcation is the basic mechanism by which fixed points are created and destroyed. As a parameter is varied, two fixed points move toward each other, collide, andmutually annihilate.
A subcritical pitchfork bifurcation occurs when there is a single unstable fixed point present, which after the change of parameters becomes unstable, and two new symmetric unstable fixed points appear.
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Nonlinear Dynamics and Chaos
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning