# Bifurcation values for logistic map

• sumonmumu
In summary, to find the r values for the first 2 bifurcations, the process involves setting rx(1−x)=0 to find x, using the x values to find r=0 and r=1, and then setting dx/dt = 0 to find the bifurcation value. The equation f(x)=rx(1−x) is different from dx/dt = 0. The notation used may be confusing, but setting f(x)=0 is not significant just because there is a zero.
sumonmumu

## Homework Statement

Find numerically the r values for the first 2 bifurcations.

## Homework Equations

xi+1 = f(xi), f(x) = rx(1 − x)

## The Attempt at a Solution

To find the values of r, first I set rx(1−x)=0 to find x and then used the x values to find r=0 and r=1. But, I am still confused. Do you think what I did here is correct? If not, can you help me find the mistakes here?

first I set rx(1−x)=0 to find x
Why =0? What is special about 0?

To find the bifurcation value, you have to set dx/dt = 0. That's the speciality.

dx/dt = 0 is different from your equation.

f(x) = dx/dt here.

Okay, then I don't understand your notation, but f(x)=0 is nothing special just because there is a zero.

and then used the x values to find r=0 and r=1
And I don't understand how you got that.

## 1. What is the logistic map?

The logistic map is a mathematical model used to describe the population growth of a species over time. It is a discrete dynamical system that is commonly used in chaos theory and population biology.

## 2. What are bifurcation values in the logistic map?

Bifurcation values in the logistic map refer to the points at which the behavior of the system changes from stable to chaotic. These values occur when the parameter in the logistic map, known as the growth rate or r, is varied.

## 3. How are bifurcation values calculated in the logistic map?

Bifurcation values in the logistic map can be calculated by varying the growth rate parameter r and observing the behavior of the system over time. As the value of r increases, the system will exhibit a period-doubling cascade, leading to chaos at certain values of r.

## 4. What is the significance of bifurcation values in the logistic map?

The significance of bifurcation values in the logistic map lies in their relationship to chaos theory and the study of complex systems. These values represent a critical point at which the behavior of the system changes drastically, and studying them can provide insights into the nature of chaotic systems.

## 5. Can bifurcation values be predicted in the logistic map?

While it is possible to calculate bifurcation values for the logistic map, it is not always possible to predict them exactly. This is due to the sensitive nature of chaotic systems and their dependence on initial conditions. However, by studying the behavior of the system and analyzing the bifurcation values, we can gain a deeper understanding of the dynamics at play.

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