File:GM map phase space plot 1.png

English: A strange attractor of Gumowski-Mira map given by the 2-dimensional discrete dynamical system:

${\displaystyle x_{n+1}=y_{n}+\alpha y_{n}(1-\sigma y_{n}^{2})+g(x_{n}),}$

${\displaystyle y_{n+1}=-x_{n}+g(x_{n+1}).}$

Where,

${\displaystyle g(x)=\mu x+{\frac {2(1-\mu )x^{2}}{1+x^{2}}}}$

The parameters are α = 0.008, σ = 0.05, μ = −0.496. The initial values are x₀ = 1, y₀ = 1. The diagram is showing the plots of iterations from n = 2000 to n = 100000.