Ordinary differential equations: Bifurcations
Bifurcations and bifurcation diagrams
We consider the differential equation where is some function and a parameter. The figure below shows the graphs of the right-hand side of the differential equation as a function of for four different parameter values, namely for , , and . For values of between and the functions change neatly so that the graphs will always lie neatly between the graphs shown.


Which bifurcation value, named , can be deduced from the shown graphs?
The number of equilibria changes in the bifurcation:
for the number of equilibria is equal to
for the number of equilibria is equal to
Select the right elements from the following drop-down menus so that you finally get the phase line of this differential equation.at the bifurcation value .
The number of equilibria changes in the bifurcation:
for the number of equilibria is equal to
for the number of equilibria is equal to
Select the right elements from the following drop-down menus so that you finally get the phase line of this differential equation.at the bifurcation value .
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