Supercritical pitchfork bifurcation

Example 3: Consider

For p >0, there are two nontrivial equilibria, x = iy/p. The transition stability is illustrated in Figure 6 (left). In eqn [4], there is a symmetry: replacing x !—x yields the same differential equation - that is, the equation is invariant with respect to the transformation x !—x. The symmetry of the differential equation is also found in the stationary solutions. Apart from x !—x the two half-branches emanating from (x0, p0) = (0, 0) are identical and thus can be identified. Symmetry plays a crucial role for several bifurcation phenomena.

- - J


Figure 6 Pitchfork bifurcation. Left: supercritical bifurcation of x = px-x3; Right: subcritical bifurcation of x = px+x3.

10 Ways To Fight Off Cancer

10 Ways To Fight Off Cancer

Learning About 10 Ways Fight Off Cancer Can Have Amazing Benefits For Your Life The Best Tips On How To Keep This Killer At Bay Discovering that you or a loved one has cancer can be utterly terrifying. All the same, once you comprehend the causes of cancer and learn how to reverse those causes, you or your loved one may have more than a fighting chance of beating out cancer.

Get My Free Ebook

Post a comment