Discretized locally active memristor and application in logarithmic map

Compared with continuous memristor, discrete memristor is more suitable for the application of memristor in discrete system. However, discrete memristor has not been fully appreciated. In this paper, a discrete memristor is obtained by discretizing continuous memristor based on the rectangular pulse discrete sampling method (RPDSM), and it satisfies the definition of generalized memristor by identifying fingerprint characteristics. The perfect matching of the v-i curves for appropriate sampling period further confirms the correctness of discretization result. Power-off plot and DC V-I plot are utilized to dissect the volatility and local activity of the memristor. Then, a new discrete memristive map, called DLAM-Log map for short, is constructed by coupling the discretized locally active memristor and logarithmic function. It shows that the DLAM-Log map can generate complex dynamics such as robust chaos, coexisting multiple attractors and some special transient dynamics. Finally, a practical modulation scheme of signal amplitude and functional type is proposed by introducing control function into the DLAM-Log map. The feasibility of the modulation scheme is theoretically interpreted and numerically validated, which shows potential significance in chaos-based information engineering.

Automated summary

This paper discretizes continuous memristor to obtain a discrete memristor using the rectangular pulse discrete sampling method. By identifying fingerprint characteristics, it satisfies the definition of a generalized memristor. The resulting DLAM-Log map generates complex dynamics and a modulation scheme is proposed, showing potential significance in chaos-based information engineering.