A fractional-order Chua's system: System model, numerical simulations, hidden dynamics, DSP implementation and voice encryption application

In this paper, a fractional-order Chua's system with exponential nonlinearity is proposed and its complex dynamics, DSP implementation and voice encryption application are carried out to show its potential application value in the field of information security. Firstly, dynamics is analyzed by means of phase diagram, bifurcation, Lyapunov exponents, basin attraction and complexity measure. The system is solved by two different methods which give different analysis results. And it shows that the system contains rich nonlinear dynamical behaviors with derivative order and system parameters varying. Secondly, the system is realized using the DSP (Digital Signal Processor) digital circuit and a chaotic pseudo-random sequence generator is designed and tested for further applications. Thirdly, a voice encryption scheme is proposed by the coupled synchronization, thus the receiver does not need to know the keys from the sender and the sender keeps the key and guarantees the security. Meanwhile, after position scrambling and value encryption, the performance analysis shows the effectiveness of the proposed encryption algorithm.