4.3 Logistic Map 1 Flashcards
1
Q
How many dimensions does a continuous system need for chaos?
A
At least 2D
2
Q
Why can the 1D tent map have chaos?
A
Due to the divergence of trajectories due to the non-invertability of it
3
Q
State the Logistic map equation, and define all terms in it
A
x_N+1 = λx_N ( 1 - x_N)
λ > 0 - Birth rate
-λx_N ^2 - saturation term
4
Q
What must we assume about x_N in the logistic map equation?
A
x_N must have a continuous limit i.e. x(t)
5
Q
What values are lambda and x bounded between?
A
x is bounded between 0 and 1
Lambda is bounded between 1/4
Peak occurs at x = 1/2 where M(1/2) = lambda / 4
6
Q
What does the logistic map transform to when lambda = 4?
A
The tent map
7
Q
What type of behaviour do we have at lambda = 4?
A
Global chaos
