File:Synchronization and intermittency of coupled logistic maps.png

English: Intermittency phenomena generated by the following coupled map model

${\displaystyle {\begin{cases}x_{n+1}=f(x_{n})+D(f(y_{n})-f(x_{n}))\\y_{n+1}=f(y_{n})+D(f(x_{n})-f(y_{n}))\end{cases}}}$

The following logistic map is used for the above functions f(x) and f(y).

${\displaystyle f(x)=ax(1-x)}$

The applied parameters are D = 0.43 and a = 3.8. The initial values are x₀ = 0.403570618398365 and y₀ = 0.5000126012101. The two variables x_n and y_n synchronize each other (namely |x_n − y_n| is almost equal to zero) in the range of n < 4170, but the synchronization breaks in the range of 4170 < n < 4270, then the two variables synchronize each other again in the range of 4270 < n.