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High-performance reservoir computing has to rely on its highly rich internal dynamic. Chaotic systems based on memristors are widely employed in reservoir computing because of their wealthy nonlinear dynamic behaviors, but there are few studies and applications related to discrete memristor models compared to continuous memristor models. This paper proposes a brand new discrete memristor model, and a two-dimensional hyper chaotic maps is constructed by coupling the discrete memristor model and a sinusoidal function. The map has rich nonlinear dynamic behaviors which cater to the need for RC, therefore, we apply this map to enhance the richness of the state of the reservoir, and test the reservoir's computing capability by the emulation of NARMA and Santa Fe time series prediction task. For this purpose, using the method of the single node with delayed feedback, the proposed reservoir can avoid the selection of meta-parameters, and fully exploits the time dependence of the map states to replace the interactions between the internal nodes. As far as we know, this is the first time that time series analysis using the discrete memristive map, and the experimental results demonstrate that the hyperchaotic map based on the discrete memristor can effectively optimize the performance of the reservoir computing. Moreover, the proposed reservoir shows several attractive features including simple design, ease to calculate, and robustness. [ABSTRACT FROM AUTHOR]

At present, researchers only find that memristor-based time-delay (MBTD) chaotic systems have rich dynamic behaviors. However, there are still many difficulties in the analysis and application of the MBTD chaotic system. Therefore, a novel 3-D MBTD chaotic system with extreme multi-stability and line equilibrium points is proposed in this work. First, by applying dynamic analysis and numerical simulation, basic behaviors of the system are employed to illustrate the superiority of the system. Then, some special nonlinear phenomena are observed by two-parameter bifurcation diagrams, such as coexisting hidden attractors of both periodic and chaotic, coexisting multi-scroll hidden attractors, coexisting single-scroll hidden attractors and coexisting periodic attractors, which mean that hidden extreme multi-stability occurs. Moreover, the system which has good autocorrelation and cross-correlation is applied to generate the chaotic pseudo-random sequence. Finally, the approximate entropy of the chaotic pseudo-random sequence is larger than that of other time-delay chaotic systems. The above manifest that this MBTD chaotic system possesses abundant dynamics and good randomness. Hence this system owns latent force in the application of memristor. [ABSTRACT FROM AUTHOR]