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In bifurcation theory, a field within mathematics, a transcritical bifurcation is a particular kind of local bifurcation, meaning that it is characterized...

flip) bifurcation, and otherwise, it is a Hopf bifurcation. Examples of local bifurcations include: Saddle-node (fold) bifurcation Transcritical bifurcation...

context of a biological system, bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the...

mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed...

t}}=\mu +x^{2}} where μ {\displaystyle \mu } is the bifurcation parameter. The transcritical bifurcation d x d t = r ln ⁡ x + x − 1 {\displaystyle {\frac...

of the scaled bifurcation equation is called the algebraic bifurcation equation, and the implicit function theorem applied the bifurcation equations states...

bifurcation; and the transcritical or asymmetric bifurcation. All but the first of these examples is a form of pitchfork bifurcation. Simple models for...

behavior), while transcritical and pitchfork bifurcations break down in the presence of imperfections. Thus, the only one-dimensional bifurcation that can exist...

behavior), while transcritical and pitchfork bifurcations break down in the presence of imperfections. Thus, the only one-dimensional bifurcation that can exist...