The randomness of chaos comes from its sensitivity to initial conditions, which can be used for cryptosystems and secure communications. The Lyapunov exponent is a typical measure of this sensitivity. In this paper, for a given discrete chaotic system, a cascading method is presented for constructing a new discrete chaotic system, which can significantly enlarge the maximum Lyapunov exponent and improve the complex dynamic characteristics. Conditions are derived to ensure the cascading system is chaotic. The simulation results demonstrate that proper cascading can significantly enlarge the system parameter space and extend the full mapping range of chaos. These new features have good potential for better secure communications and cryptography.
In this paper, a new memristor model is proposed and the corresponding emulator is presented to explore its electrical characteristics. A memristive chaotic circuit is designed based on this memristor and a capacitor, which has a conservative nature. The dynamic properties of the system, including high sensitivity to initial values and parameters, coexisting orbits, and transient phenomena, are obtained and investigated by Lyapunov exponents and phase volumes. The chaotic characteristics of the system are confirmed by circuit simulations and experimental devices, which illustrate the validity of the theoretical analyses. Furthermore, a random sequence generator is developed to explore the potential application of the circuit.
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