Chaotic dynamical systems with hard proposition

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How I can prove this proposition ?

proposition : Consider a network with a fixed connection topology, having in each node identical members of the family of m-modal functions f in the real interval. Then:

1)The synchronizability decreases when the topological entropy $ h_{top}(f) $, in each node, increases

2)There is a threshold value $h_0$ of the topological entropy $h_{top}(f) $ such that

for each f in this family, with topological entropy $ h<h_0 $ the synchronization interval of the network with f in each node is nonempty.

I would be interest for any replies or any comments