(x_n+1 y_n+1) = (-a x_n^2 + y_n + 1 b x_n) (n = (0, 1, 2, ...))

initial condition x_0 | 0.6 initial condition y_0 | 0.2 parameter a | 1.4 parameter b | 0.3

n | 0 | 1 | 2 | 3 | 4 (x_n y_n) | (0.60000 0.20000) | (0.69600 0.18000) | (0.50182 0.20880) | (0.85625 0.15055) | (0.12411 0.25688)

correlation dimension | 1.25

chaotic

λ≈0.418

(b fixed at 0.3)

(a fixed at 1.4)

(x_n y_n) = (y_n+1/b (a y_n+1^2)/b^2 + x_n+1 - 1)≈(3.33333 y_n+1 15.5556 y_n+1^2 + x_n+1 - 1)

x_n+1 = -a x_n^2 + b x_n-1 + 1 = -1.4 x_n^2 + 0.3 x_n-1 + 1

position | ((b - sqrt((b - 1)^2 + 4 a) - 1)/(2 a) (b (b - sqrt((b - 1)^2 + 4 a) - 1))/(2 a))≈(-1.13135 -0.339406)

position | ((b + sqrt((b - 1)^2 + 4 a) - 1)/(2 a) (b (b + sqrt((b - 1)^2 + 4 a) - 1))/(2 a))≈(0.631354 0.189406)