What causes period doubling bifurcation?

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 the constant value of Feigenbaum number?

about 4.6692016
Behind the Feigenbaum Constant It’s called the Feigenbaum constant, and it’s about 4.6692016. And it shows up, quite universally, in certain kinds of mathematical—and physical—systems that can exhibit chaotic behavior.

Where does the Feigenbaum constant come from?

This constant—named after the mathematician Mitchell Feigenbaum—refers to a certain property of chaotic systems, the kinds of systems that Jeff Goldblum goes on about in Jurassic Park.

Who discovered the period doubling cascade?

Myrberg
The first is an individual period-doubling bifurcation. The second is an infinite collection of period doublings that are connected together by periodic orbits in a pattern called a cascade. It was first described by Myrberg and later in more detail by Feigenbaum.

What is a flip bifurcation?

1. A period doubling bifurcation in a discrete dynamical system. It is a bifurcation in which the system switches to a new behavior with twice the period of the original system. That is, there exists two points such that applying the dynamics to each of the points yields the other point.

What does Feigenbaum mean?

Jewish (Ashkenazic): ornamental name from German Feigenbaum ‘fig tree’.

When was Feigenbaum constant discovered?

1978
The Feigenbaum universal constant, \delta is discovered in 1978 and it is found to occur in many period doubling bifurcation phenomena in the celebrated logistic map and the Lorenz differential equation system with chaotic (or aperiodic) solutions.

Is Feigenbaum constant transcendental?

Properties. Both numbers are believed to be transcendental, although they have not been proven to be so. There is also no known proof that either constant is irrational.

What is bifurcation in dynamical systems?

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.

What does Feigenbaum mean by Total Quality Control?

He wrote, “Total quality control is an effective system for integrating the quality development, quality maintenance, and quality improvement efforts of the various groups in an organization so as to enable production and service at the most economical levels which allow full customer satisfaction.”

When did a.v.feigenbaum become an honorary member?

The name Armand V. Feigenbaum and the term “total quality control” are virtually synonymous. In 1986, when the ASQ board of directors elected Feigenbaum an Honorary member, it acknowledged a career of more than 35 years in the quality field.

How old was Armand Vallin Feigenbaum when he died?

Armand Vallin Feigenbaum (April 6, 1920 – November 13, 2014) was an American quality control expert and businessman. He devised the concept of Total Quality Control which inspired Total Quality Management .

What did a.v.feigenbaum do before General Electric?

Prior to assuming his responsibilities at General Systems Co., Feigenbaum was the manager of worldwide manufacturing operations and quality control for the General Electric Co. Feigenbaum is recognized as an innovator in the area of quality cost management.