Concept explainers
Interpretation:
For the given function
Concept Introduction:
Bifurcation theory is used to study the stability of dynamical systems.
The phenomenon in which fixed points are created and destroyed by varying the control parameter is termed as saddle-node bifurcation.
The transcritical bifurcation occurs when the fixed points exchange their stabilities as the parameter is changed.
Fixed points are the points where,
A pitchfork bifurcation occurs where the system transitions from one fixed point to three fixed points.
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 are stable.
A supercritical pitchfork bifurcation occurs when there is a single stable fixed point present, which after the change of parameters becomes unstable, and two new symmetric fixed points appear are stable.
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Nonlinear Dynamics and Chaos
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,