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The ultimate state of projective synchronization is usually considered to be hardly controllable due to its close dependence on the initial conditions of both drive and response systems. In this letter, we show that the scaling factor of projective synchronization can be controlled to be proportional to a given scalar function with respect to time even without the knowledge of the initial conditions of response system. Further, we apply it to the chaotic encryption. Comparing with some existing implementations, it is found that the present scheme owns several remarkable advantages. To our knowledge, it is for the first time that the projective synchronization is applied to chaos-based encryption.

The phenomenon of tunneling is well-known in quantum theory, however, many novel characteristics appear when the corresponding classical dynamics of the underlying system is chaotic. In this paper, the chaos-assisted tunneling is found in a triple-well potential under an external periodic driving field. We make use of the Husimi distribution to illustrate this characteristic in the quantum phase-space.

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