Feigenbaum Constant (δ)

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Definition

The Feigenbaum constant δ is a universal constant in chaos theory, the limiting ratio between bifurcation points.

δ = lim_n → ∈fty \fraca_n-1 - a_n-2aₙ - a_n-1 ≈ 4.6692016...

Limit of bifurcation ratios

α ≈ 2.5029...

Second Feigenbaum constant (scaling)

Example 1

In logistic map x_{n+1} = rx_n(1-x_n), what's the ratio of bifurcation r values?

Discovered by: Mitchell Feigenbaum (1975)

Key discovery in chaos theory, showing universal properties of nonlinear systems.

Bifurcation analysis

Turbulence, nonlinear oscillations

Population dynamics