  We consider a chain of oscillators with hyperbolic chaos coupled via
diffusion. When the coupling is strong the chain is synchronized and
demonstrates hyperbolic chaos so that there is one positive Lyapunov exponent.
With the decay of the coupling the second and the third Lyapunov exponents
approach zero simultaneously. The second one becomes positive, while the third
one remains close to zero. Its finite-time numerical approximation fluctuates
changing the sign within a wide range of the coupling parameter. These
fluctuations arise due to the unstable dimension variability which is known to
be the source for non-hyperbolicity. We provide a detailed study of this
transition using the methods of Lyapunov analysis.
