Sorry for that question with incomplete information.
x(t^1, t^2) is a bivariate sequence (discrete multitime recurrences)
1\alpha has 1 on the position alpha and 0 otherwise. 1 = (0, . . . , 0, 1, 0, . . . , 0) ∈ Z^m
We introduce a two-time logistic map as a recurrence relation of degree 2,
x(t + 1\alpha) = r*x(t)*(1 - x(t)); t = (t^1; t^2)∈N^2; x(t) ∈ R; \alpha = 1, 2;
where x(t) is a number between zero and one that represents the ratio of
existing population to the maximum possible population.
This two-time recurrence is an archetypal example of how complex, chaotic
behavior can arise from very simple non-linear recurrence equations.
If r = 2, then the solution is
x(t) =1/2-1/2*(1-2x0)^2^(t1+t2), for x0 in [0,1)