A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata. (October 2021) - Dong, Youheng; Zhao, Geng
Highlights: We propose a spatiotemporal chaotic system, a novel pseudo-random CML (PRCML) system, with the pseudo-random coupling method based on the elementary cellular automata (ECA), and add different perturbations to lattices in each iteration according to the ECA. In addition, the innovations of the proposed system are listed as follows: First of all, the pseudo-random coupling is utilized in proposed system. Rather than employing the adjacent lattices for coupling as a conventional CML, the PRCML's choice of lattices for coupling is innovatively dependent on the iterative result of the ECA which is in chaos. Furthermore, the choice of lattices for coupling is always changing in each iteration because the ECA is iterated with the system. Thus, the coupling is pseudo-random that enhance the complexity of the system. Another innovation is that the iterative result of the ECA is employed for disturbing the PRCML. This novel scheme leads to the following advantages: Firstly, the periodic windows in bifurcation diagram fade out obviously. Secondly, the ECA is essentially a discrete dynamical system, and the finite computing precision has no influence on it. Thus, employing iterative results of the ECA as the perturbation alleviates dynamical degradation efficiently. Thirdly, owing to the different pseudo-random perturbation for each lattice, the correlation between any two lattices is significantly reduced. Theory analysis and simulation test indicate that the new system has better performance in complexity, ergodic and unpredictability than other CML systems such as adjacent CML and nonlinear CML based on fractional order logistic equation, etc. Furthermore, the correlation coefficient between any two lattices in proposed system is significantly lower than other systems. Abstract: The coupled map lattices (CML) is a spatiotemporal chaotic system with complex dynamic behavior. In this paper, we propose a spatiotemporal chaotic system with a novel pseudo-random coupling method based on elementary cellular automata (ECA), and introduce different perturbations into lattices in each iteration according to ECA. We investigate the spatiotemporal dynamic properties and chaotic behaviors of the proposed system such as bifurcation diagrams, Kolmogorov Sinai entropy, and uniformity. Moreover, the randomness of sequences generated by the proposed system and the correlation between any two lattices are discussed. Theory analyses and simulations indicate that the new system has better performance in complexity, ergodic and unpredictability than other CML systems such as adjacent CML and nonlinear CML based on fractional order logistic equation, etc. Furthermore, the correlation coefficient between any two lattices in the proposed system is significantly lower than other systems, and another advantage of the proposed system is utilizing the output of ECA to perturb the chaotic system which can effectively alleviate the dynamical degradation in digital system. The excellent performance of the proposed system demonstrates that it has great potential for crypto-system.