DIFFERENTIAL EQUATIONS Can someone please explain what a bif

DIFFERENTIAL EQUATIONS:

Can someone please explain what a bifurcation point is and what it does for a function? In *words* please.

Thank y ou

Solution

The simple meaning of bifurcation means to split apart take an example of differential equation

dy/dt = Ay^2, in this case the equilibrium point depends on the sign of A, if the value of A is zero, then there is only one equilibrium point

If A>0, there will be two equilibrium points

Hence the value of A will bifurcate the graph of f(x,y) or the slope field, hence we can say that family of curves have bifurcation if the value of A is greater than zero