To make a simple example of a system that can synchronize even
when chaotic, take N logistic maps
and couple each to its nearest neighbors. Letting 
x^{1}_{t}, ...,
x^{N}_{t} 
stand for populations 1, ..., N in generation t, we obtain the populations in
generation t+1 by 
x^{1}_{t+1}  =  (1c)L(x^{1}_{t}) +
(c/2)(L(x^{N}_{t}) + L(x^{2}_{t})) 
x^{2}_{t+1}  =  (1c)L(x^{2}_{t}) +
(c/2)(L(x^{1}_{t}) + L(x^{3}_{t})) 
x^{3}_{t+1}  =  (1c)L(x^{3}_{t}) +
(c/2)(L(x^{2}_{t}) + L(x^{4}_{t})) 
 ...  
x^{N1}_{t+1}  =  (1c)L(x^{N1}_{t}) +
(c/2)(L(x^{N2}_{t}) + L(x^{N}_{t})) 
x^{N}_{t+1}  =  (1c)L(x^{N}_{t}) +
(c/2)(L(x^{N1}_{t}) + L(x^{1}_{t})) 

This configuration is an example of a coupled
map lattice. Graphically, we have 

Here c is the coupling constant,
a measure how how strongly
each value depends on its neighbors. For examaple, 
c = 0 gives N
independent logistic maps: each depends only on itself, and 
c = 1 given maps that depend not on their past, but on the
past of their neighbors. 
