Violations of Bell's inequality in synchronized hyperchaos

Motivated by a parallel between quantum cryptography and chaos synchronizat ion cryptography, we construct a Bell's inequality for a pair of synchronou sly coupled variable-order Generalized Rossler Systems, with arbitrarily bi narized final states. In the infinite-order limit, although dynamical param eters cannot be extracted from the coupling signal in finite time, the ineq uality is violated, as with entangled quantum states. The violations are we aker than in quantum theory, vanishing as the differences between correspon ding parameters of the coupled systems become small. The fact that Bell's i nequality can be violated for a pair of classical systems that are not disc ernibly connected supports the possibility of a realist interpretation of q uantum mechanics.