A locally active discrete memristor model and its application in a hyperchaotic map

© 2022 Springer Nature Switzerland AG. Part of Springer Nature. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-021-07132-5The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.Peer reviewedFinal Accepted Versio

Everything You Wish to Know About Memristors But Are Afraid to Ask

This paper classifies all memristors into three classes called Ideal, Generic, or Extended memristors. A subclass of Generic memristors is related to Ideal memristors via a one-to-one mathematical transformation, and is hence called Ideal Generic memristors. The concept of non-volatile memories is defined and clarified with illustrations. Several fundamental new concepts, including Continuum-memory memristor, POP (acronym for Power-Off Plot), DC V-I Plot, and Quasi DC V-I Plot, are rigorously defined and clarified with colorful illustrations. Among many colorful pictures the shoelace DC V-I Plot stands out as both stunning and illustrative. Even more impressive is that this bizarre shoelace plot has an exact analytical representation via 2 explicit functions of the state variable, derived by a novel parametric approach invented by the author

A Triple-Memristor Hopfield Neural Network With Space Multi-Structure Attractors And Space Initial-Offset Behaviors

© 2023 IEEE. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TCAD.2023.3287760Memristors have recently demonstrated great promise in constructing memristive neural networks with complex dynamics. This paper proposes a memristive Hopfield neural network with three memristive coupling synaptic weights. The complex dynamical behaviors of the triple-memristor Hopfield neural network (TM-HNN), which have never been observed in previous Hopfield-type neural networks, include space multi-structure chaotic attractors and space initial-offset coexisting behaviors. Bifurcation diagrams, Lyapunov exponents, phase portraits, Poincaré maps, and basins of attraction are used to reveal and examine the specific dynamics. Theoretical analysis and numerical simulation show that the number of space multi-structure attractors can be adjusted by changing the control parameters of the memristors, and the position of space coexisting attractors can be changed by switching the initial states of the memristors. Extreme multistability emerges as a result of the TM-HNN’s unique dynamical behaviors, making it more suitable for applications based on chaos. Moreover, a digital hardware platform is developed and the space multi-structure attractors as well as the space coexisting attractors are experimentally demonstrated. Finally, we design a pseudo-random number generator to explore the potential application of the proposed TM-HNN.Peer reviewe

Memristors for the Curious Outsiders

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page