Example 2: Consider the planar system x = px-x1, y = -y, (x,y)pR2, ppR [3]

For p <0, there is a stable node point O (0, 0) and a saddle A (p, 0), and for p = 0, there is a nonhyperbolic equilibrium point O (0, 0) (saddle-node point). For p >0, there is a

Saddles

\ Unstable nodes

Stable nodes

Saddles

Figure 4 Saddle-node bifurcation of x = p—x2, y=x—cy.

Figure 5 Transcritical bifurcation of x = px-x2, y = -y.

stable node point A (p, 0) and a saddle 0 (0, 0). It is easy to know that the stability of 0 and A at p = 0 have commuted. The bifurcation diagram is displayed in Figure 5.

Was this article helpful?

You Might Start Missing Your Termites After Kickin'em Out. After All, They Have Been Your Roommates For Quite A While. Enraged With How The Termites Have Eaten Up Your Antique Furniture? Can't Wait To Have Them Exterminated Completely From The Face Of The Earth? Fret Not. We Will Tell You How To Get Rid Of Them From Your House At Least. If Not From The Face The Earth.

## Post a comment