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Inspired by the chaotic waterwheel invented by Malkus and Howard about 40 years ago, we have developed a gas turbine that randomly switches the sense of rotation between clockwise and counterclockwise. The nondimensionalized expressions for the equations of motion of our turbine are represented as a starlike network of many Lorenz subsystems sharing the angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We show qualitative similarities between the statistical properties of the angular velocity of the turbine rotor and the velocity field of large-scale wind in turbulent Rayleigh-Bénard convection reported by Sreenivasan et al. [Phys. Rev. E 65, 056306 (2002)]. Our equations of motion achieve the random reversal of the turbine rotor through the stochastic resonance of the angular velocity in a double-well potential and the force applied by rapidly oscillating fields. These results suggest that the augmented Lorenz model is applicable as a dynamical model for the random reversal of turbulent large-scale wind through cessation.

We have recently developed a chaos-based stream cipher based on augmented Lorenz equations as a star network of Lorenz subsystems. In our method, the augmented Lorenz equations are used as a pseudorandom number generator. In this study, we propose a new method based on the augmented Lorenz equations for generating binary pseudorandom numbers and evaluate its security using the statistical tests of SP800-22 published by the National Institute for Standards and Technology in comparison with the performances of other chaotic dynamical models used as binary pseudorandom number generators. We further propose a faster version of the proposed method and evaluate its security using the statistical tests of TestU01 published by L'Ecuyer and Simard.

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Inspired by the augmented Lorenz equations, we have designed a star network of Rössler oscillators, referred to as augmented Rössler equations, in which each Rössler oscillator is coupled with the other oscillators via a single variable y as the central node of the whole network. We investigate the dynamical nature of the augmented Rössler equations in terms of the bifurcation diagram of a single augmented Rössler oscillator and the chaotic synchronizability of coupled augmented Rössler oscillators, and show that intermittent synchronization between identical augmented Rössler oscillators as well as partial synchronization between nonidentical ones can be achieved via direct coupling of the central nodes. We also show that nonidentical augmented Rössler oscillators coupled via intermittent mutual diffusive coupling exhibit partial synchrony, despite the intermittency of the diffusive coupling. We discuss possible application of such synchronous behavior in terms of chaos-based secret key distribution.