Firing multistability in a locally active memristive neuron model

Funding Information: This work is supported by The Major Research Project of the National Natural Science Foundation of China (91964108), The National Natural Science Foundation of China (61971185), The Open Fund Project of Key Laboratory in Hunan Universities (18K010). Publisher Copyright: © 2020, Springer Nature B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.The theoretical, numerical and experimental demonstrations of firing dynamics in isolated neuron are of great significance for the understanding of neural function in human brain. In this paper, a new type of locally active and non-volatile memristor with three stable pinched hysteresis loops is presented. Then, a novel locally active memristive neuron model is established by using the locally active memristor as a connecting autapse, and both firing patterns and multistability in this neuronal system are investigated. We have confirmed that, on the one hand, the constructed neuron can generate multiple firing patterns like periodic bursting, periodic spiking, chaotic bursting, chaotic spiking, stochastic bursting, transient chaotic bursting and transient stochastic bursting. On the other hand, the phenomenon of firing multistability with coexisting four kinds of firing patterns can be observed via changing its initial states. It is worth noting that the proposed neuron exhibits such firing multistability previously unobserved in single neuron model. Finally, an electric neuron is designed and implemented, which is extremely useful for the practical scientific and engineering applications. The results captured from neuron hardware experiments match well with the theoretical and numerical simulation results.Peer reviewedFinal Accepted Versio

A multi-stable memristor and its application in a neural network

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Nowadays, there is a lot of study on memristorbased systems with multistability. However, there is no study on memristor with multistability. This brief constructs a mathematical memristor model with multistability. The origin of the multi-stable dynamics is revealed using standard nonlinear theory as well as circuit and system theory. Moreover, the multi-stable memristor is applied to simulate a synaptic connection in a Hopfield neural network. The memristive neural network successfully generates infinitely many coexisting chaotic attractors unobserved in previous Hopfield-type neural networks. The results are also confirmed in analog circuits based on commercially available electronic elements.Peer reviewe

Diversified Butterfly Attractors of Memristive HNN With Two Memristive Systems and Application in IoMT for Privacy Protection

© 2024, IEEE. This is an open access accepted manuscript distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/Memristors are often used to emulate neural synapses or to describe electromagnetic induction effects in neural networks. However, when these two things occur in one neuron concurrently, what dynamical behaviors could be generated in the neural network? Up to now, it has not been comprehensively studied in the literature. To this end, this paper constructs a new memristive Hopfield neural network (HNN) by simultaneously introducing two memristors into one Hopfield-type neuron, in which one memristor is employed to mimic an autapse of the neuron and the other memristor is utilized to describe the electromagnetic induction effect. Dynamical behaviors related to the two memristive systems are investigated. Research results show that the constructed memristive HNN can generate Lorenz-like double-wing and four-wing butterfly attractors by changing the parameters of the first memristive system. Under the simultaneous influence of the two memristive systems, the memristive HNN can generate complex multi-butterfly chaotic attractors including multi-double-wing-butterfly attractors and multi-four-wing-butterfly attractors, and the number of butterflies contained in an attractor can be freely controlled by adjusting the control parameter of the second memristive system. Moreover, by switching the initial state of the second memristive system, the multi-butterfly memristive HNN exhibits initial-boosted coexisting double-wing and four-wing butterfly attractors. Undoubtedly, such diversified butterfly attractors make the proposed memristive HNN more suitable for chaos-based engineering applications. Finally, based on the multi-butterfly memristive HNN, a novel privacy protection scheme in the IoMT is designed. Its effectiveness is demonstrated through encryption tests and hardware experiments.Peer reviewe

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

Entropy analysis and image encryption application based on a new chaotic system crossing a cylinder

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents' spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system's efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shue the rows and columns of the image, and then the shued image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance. - 2019 by the authors.Scopu

Grid Multi-Butterfly Memristive Neural Network With Three Memristive Systems: Modeling, Dynamic Analysis, and Application in Police IoT

© 2024, IEEE. This is an open access accepted manuscript distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/Nowadays, the Internet of Things (IoT) technology has been widely applied in the police security system. However, with more and more image data that concerns crime scenes being transmitted through the police IoT, there are some new security and privacy issues. Therefore, how to design a safe and efficient secret image sharing solution suitable for police IoT has become a very urgent task. In this work, a grid multi-butterfly memristive Hopfield neural network (HNN) with three memristive systems is constructed and its complex dynamics are deeply analyzed. Among them, the first memristive system is modeled by emulating a self connection synapse, the second memristive system is modeled by coupling two neurons, and the third memristive system is modeled by describing external electromagnetic radiation. Dynamic analyses show that the proposed memristive HNN can not only generate two kinds of 1-directional (1D) multi-butterfly chaotic attractors but also produce complex grid (2D) multi-butterfly chaotic attractors. More importantly, by switching the initial states of the second and third memristive systems, the grid multi-butterfly memristive HNN exhibits initial-boosted plane coexisting multi-butterfly attractors. Moreover, the number of butterflies contained in a multi-butterfly attractor and coexisting attractors can be easily adjusted by changing memristive parameters. Based on these complex dynamics, an image security solution is designed to show the application of the newly constructed grid multi-butterfly memristive HNN to police IoT security. Security performances indicate the designed scheme can resist various attacks and has high robustness. Finally, the test results are further demonstrated through RPI-based hardware experimentsPeer reviewe

A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters' sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system's attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system's chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator's time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue