Transcritical bifurcation

In bifurcation theory, a field within mathematics, a transcritical bifurcation is a particular kind of local bifurcation, meaning that it is characterized by an equilibrium having an eigenvalue whose real part passes through zero. The normal form of a transcritical bifurcation is This equation is similar to the logistic equation but in this case we allow and to be positive or negative (while in the logistic equation and must be non-negative).The two fixed points are at and . When the parameter is negative, the fixed point at is stable and the fixed point is unstable. But for , the point at . For example: *

Transcritical bifurcation

In bifurcation theory, a field within mathematics, a transcritical bifurcation is a particular kind of local bifurcation, meaning that it is characterized by an equilibrium having an eigenvalue whose real part passes through zero. The normal form of a transcritical bifurcation is This equation is similar to the logistic equation but in this case we allow and to be positive or negative (while in the logistic equation and must be non-negative).The two fixed points are at and . When the parameter is negative, the fixed point at is stable and the fixed point is unstable. But for , the point at . For example: *