## Transcritical Bifurcation

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.

## Trash To Cash

This book will surely change your life due to the fact that after reading this book and following through with the steps that are laid out for you in a clear and concise form you will be earning as much as several thousand extra dollars a month, as you can see by the cover of the book we will be discussing how you can make cash for what is considered trash by many people, these are items that have value to many people that can be sold and help people who need these items most.

## Post a comment