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<noinclude>{{Scripthinweis|Mechanik|7|3}}</noinclude> Sei der Fluß von einem Kntrollparametr µ abhängig, so zeigt sich, dass sich die Zahl der Attraktoren bei einem kritischen Wert µc schlagartig ändern kann. Es treten dann sogenannte Bifurkationen auf ("Verzweigungen" der Lösungsmannigfaltigkeit). Notwendige Voraussetzung für diesen Prozess ist jedoch Nichtlinearität! Bifurkationspunkte sind oft verknüpft mit Stabilitätswechsel. Das bedeutet, die lineare Stabilität der Fixpunkte im Falle lokaler Bifurkationen muss untersucht werden. Your aitrcle perfectly shows what I needed to know, thanks! ====A2) Transkritische Bifurkation==== :<math>\dot{x}=\mu x-{{x}^{2}}</math> :<math>x*=\mu ,0</math> :<math>\begin{align} & \delta \dot{x}=\left( \mu -2x* \right)\delta x \\ & \Rightarrow \lambda =\left\{ \begin{matrix} \mu \\ -\mu \\ \end{matrix} \right. \\ \end{align}</math> Stabilitätswechsel bei µc=0 Your article was excellent and eirdute.
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