What are the types of bifurcation?

Bifurcation types

• Saddle-node (fold) bifurcation.
• Transcritical bifurcation.
• Pitchfork bifurcation.
• Period-doubling (flip) bifurcation.
• Hopf bifurcation.
• Neimark–Sacker (secondary Hopf) bifurcation.

What is an example of bifurcation?

The definition of bifurcate is to split up or to divide into two different parts or branches. When a trail splits into two trails, this is an example of a time when the trail bifurcates.

Where does bifurcation occur?

Definition 1.1. In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden “qualitative” or topological change in its behaviour.

How many bifurcations are there?

In this chapter, we also discuss several types of bifurcations, saddle node, transcritical, pitchfork and Hopf bifurcation. Among these types, we especially focus on Hopf bifurcation. The first three types of bifurcation occur in scalar and in systems of differential equations.

What is bifurcation used for?

Bifurcation is based on the verb bifurcate, which means to divide or fork into two branches. These words are most often used in technical and scientific contexts, such as engineering and medicine.

What is artery bifurcation?

Bifurcation lesions occur when the atherosclerotic plaque involves the origin of two separate arteries. A bifurcation is defined as a division of a main, parent branch into two daughter branches of at least 2.0 mm.

Why does bifurcate mean?

: to divide into two branches or parts The stream bifurcates into two narrow channels.

What is called period doubling?

From Wikipedia, the free encyclopedia. In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system’s parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original.

What is bifurcation chaos?

In a dynamical system, a bifurcation is a period doubling, quadrupling, etc., that accompanies the onset of chaos. It represents the sudden appearance of a qualitatively different solution for a nonlinear system as some parameter is varied.

What is Carina in cardiology?

Carina is the most important anatomic structure in a bifurcation zone . It acts like a grade separator. Diverting and deflecting blood flow . The length and angle of this grade separator determine the ostial shape as well . A right angled side branch will have a circular ostium .

What is a coronary bifurcation?

A bifurcation is defined as a division of a main, parent branch into two daughter branches of at least 2.0 mm. Bifurcation lesions in coronary artery disease (CAD) are common, encompassing 15-18% of lesions treated with percutaneous coronary intervention (PCI).

What are the two types of bifurcations of γ?

Provided c > c∗is large enough, there are two bifurcations as a function of γ, which we call γ±(c). These are shown as the dashed blue lines in figure 2.9 for c = 9. Both bifurcations are of the saddle-node type.

What are the two bifurcations of the N-intercept?

The n-intercept is c and the y-intercept is γ. Provided c > c∗is large enough, there are two bifurcations as a function of γ, which we call γ±(c). These are shown as the dashed blue lines in figure 2.9 for c = 9. Both bifurcations are of the saddle-node type.

How do you find the bifurcation of a curve?

Both bifurcations are of the saddle-node type. We determine the curves γ±(c) by requiring that h(n) is tangent to y(n), which gives two equations: h(n) = n n2+1 = γ 1− n c = y(n) h′(n) = 1−n2 (n2+1)2 = − γ c = y′(n) . (2.23)

What is the normal form of pitchfork bifurcation?

2.1.3 Pitchfork bifurcation The pitchfork bifurcation is commonly encountered in systems in which there is an overall parity symmetry (u → −u). There are two classes of pitchfork: supercritical and subcritical. The normal form of the supercritical bifurcation is u˙ = ru−u3, (2.8) which has fixed points at u∗= 0 and u∗= ± √ r.