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On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke dimension, and equilibrium stability of the chaotic model are studied. Subsequently, we explore the construction of the 5D FOMHS, introducing the definitions of the Caputo differential operator and the Riemann–Liouville integral operator and employing the Adomian resolving approach to decompose the linears, the nonlinears, and the constants of the system. The complex dynamic characteristics of the system are analyzed by phase diagrams, Lyapunov exponent spectra, time-domain diagrams, etc. Finally, the hardware circuit of the proposed 5D FOMHS is performed by FPGA, and its randomness is verified using the NIST tool. [ABSTRACT FROM AUTHOR]

Since the Lorenz chaotic system was discovered in 1963, the construction of chaotic systems with complex dynamics has been a research hotspot in the field of chaos. Recently, memristive Hopfield neural networks (MHNNs) offer great potential in the design of complex, chaotic systems because of their special network structures, hyperbolic tangent activation function, and memory property. Many chaotic systems based on MHNNs have been proposed and exhibit various complex dynamical behaviors, including hyperchaos, coexisting attractors, multistability, extreme multistability, multi-scroll attractors, multi-structure attractors, and initial-offset coexisting behaviors. A comprehensive review of the MHNN-based chaotic systems has become an urgent requirement. In this review, we first briefly introduce the basic knowledge of the Hopfiled neural network, memristor, and chaotic dynamics. Then, different modeling methods of the MHNN-based chaotic systems are analyzed and discussed. Concurrently, the pioneering works and some recent important papers related to MHNN-based chaotic systems are reviewed in detail. Finally, we survey the progress of MHNN-based chaotic systems for application in various scenarios. Some open problems and visions for the future in this field are presented. We attempt to provide a reference and a resource for both chaos researchers and those outside the field who hope to apply chaotic systems in a particular application. [ABSTRACT FROM AUTHOR]

Neural networks have been widely and deeply studied in the field of computational neurodynamics. However, coupled neural networks and their brain-like chaotic dynamics have not been noticed yet. In this article, we focus on the coupled neural network-based brain-like initial boosting coexisting hyperchaos and its application in biomedical image encryption. We first construct a memristive-coupled neural network (MCNN) model based on two subneural networks and one multistable memristor synapse. Then we investigate its coupling strength-related dynamical behaviors, initial states-related dynamical behaviors, and initial-boosted coexisting hyperchaos using bifurcation diagrams, phase portraits, Lyapunov exponents, and attraction basins. The numerical results demonstrate that the proposed MCNN not only can generate hyperchaotic attractors with high complexity but also can boost the attractor positions by switching their initial states. This makes the MCNN more suitable for many chaos-based engineering applications. Moreover, we design a biomedical image encryption scheme to explore the application of the MCNN. Performance evaluations show that the designed cryptosystem has several advantages in the keyspace, information entropy, and key sensitivity. Finally, we develop a field-programmable gate array test platform to verify the practicability of the presented MCNN and the designed medical image cryptosystem. [ABSTRACT FROM AUTHOR]

Time interval between stimuli plays a critical role in Pavlov classical conditioning. In this paper, a full-functional memristive Pavlov associative memory circuit with inter-stimulus interval effect is proposed. Compared with previous works, the proposed circuit extends the Pavlov associative memory with time interval to three complex situations of conditioning and realizes bionic associative memory learning curves called inter-stimulus interval effect. On this basis, the phenomena related to time interval in classical conditioning, blocking and facilitation, are implemented. PSPICE is used to simulate the whole circuit, and the simulation results demonstrate above functions. Furthermore, an application on classification is extended on the basis of the proposed circuit. The application circuit is also verified by the simulation results in PSPICE. This paper provides a reference to associative memory based on memristor in complex time situations. [ABSTRACT FROM AUTHOR]

Emotional intelligence plays an important role in artificial intelligence. The brain circuitry of emotion mainly includes the prefrontal cortex, the amygdala, hippocampus and et al. Many brain emotional learning (BEL) models were proposed in recent years, the existing BEL models failed to consider the contextual information in practical applications, and do not discuss the corresponding circuit implementation. In this article, a context-dependent emotional learning network (CD-ELN) and its memristive circuit implementation are introduced. The added context-dependent module is used to process the contextual information, which makes the network context dependent when receiving the same input signals. For circuit implementation, the memristive circuit design mainly contains the amygdala module and orbitofrontal cortex module, which imitates the emotion learning process in the brain. Besides, a multi-input multioutput memristive circuit of the context-dependent emotional network is applied to multitask classification. PSPICE simulation results verified the adaptability and flexibility of the CD-ELN. [ABSTRACT FROM AUTHOR]

The analog circuit design of the memristive neural network (MNN), which can automatically perform the online learning algorithm, is an open question. In this article, a memristive self-learning neuron circuit for implementing the online least mean square (LMS) algorithm is designed. Extending on the designed neuron circuit, the circuit implementation of the monolayer and multilayer neural network is proposed. The proposed neural network can automatically converge the output to the set target according to the input. The application-level validations of the circuits are done using pattern recognition and license plate detection. The performances of the designed MNN circuits and the effect of memristive variation are analyzed through PSPICE simulations. The learning accuracy of the proposed circuit for license plate detection can reach 93%. Circuit simulation results reveal that the proposed MNN circuits can accelerate the training speed and have the tolerance to the variations of the memristor. [ABSTRACT FROM AUTHOR]

As a new type of nonvolatile device, the memristor has become one of the most promising technologies for designing a new generation of high-density memory. In this paper, a 4-bit high-density nonvolatile memory based on a memristor is designed and applied to image storage. Firstly, a memristor cluster structure consisting of a transistor and four memristors is designed. Furthermore, the memristor cluster is used as a memory cell in the crossbar array structure to realize the memory design. In addition, when the designed non-volatile memory is applied to gray scale image storage, only two memory cells are needed for the storage of one pixel. Through the Pspice circuit simulation, the results show that compared with the state-of-the-art technology, the memory designed in this paper has better storage density and read–write speed. When it is applied to image storage, it achieves the effect of no distortion and fast storage. [ABSTRACT FROM AUTHOR]

Memristor and activation function are two important nonlinear factors of the memristive Hopfield neural network. The effects of different memristors on the dynamics of Hopfield neural networks have been studied by many researchers. However, less attention has been paid to the activation function. In this paper, we present a heterogeneous memristive Hopfield neural network with neurons using different activation functions. The activation functions include fixed activation functions and an adaptive activation function, where the adaptive activation function is based on a memristor. The theoretical and experimental study of the neural network's dynamics has been conducted using phase portraits, bifurcation diagrams, and Lyapunov exponents spectras. Numerical results show that complex dynamical behaviors such as multi-scroll chaos, transient chaos, state jumps and multi-type coexisting attractors can be observed in the heterogeneous memristive Hopfield neural network. In addition, the hardware implementation of memristive Hopfield neural network with adaptive activation function is designed and verified. The experimental results are in good agreement with those obtained using numerical simulations. • A novel heterogeneous memristive Hopfield neural network(HMHNN) is proposed. • Complex dynamic behaviors of the new HMHNN are explored in detail. • A hardware implementation of the new HMHNN is designed. [ABSTRACT FROM AUTHOR]

In this work, a full circuit of memristor-based neural network with weighted sum simultaneous perturbation training is proposed. Firstly, a synaptic circuit is designed by using a pair of memristors, which can represent negative, zero, and positive synaptic weights. Secondly, a full circuit of the neural network is designed, with all operations being completed on the circuit without any computer aid. The neural network is trained with the weighted sum simultaneous perturbation algorithm. The algorithm does not involve complex derivative calculation and error back propagation, and it only applies perturbations to weighted sum, so the circuit implementation is more simple. Finally, application simulations of the proposed neural network circuit are performed via PSpice. The results of simulation indicate that the memristor-based neural network is practical and effective. [ABSTRACT FROM AUTHOR]

The study of dynamics on artificial neurons and neuronal networks is of great significance to understand brain functions and develop neuromorphic systems. Recently, memristive neuron and neural network models offer great potential in the investigation of neurodynamics. Many chaotic dynamics including chaos, transient chaos, hyperchaos, coexisting attractors, multistability, and extreme multistability have been researched based on the memristive neurons and neural networks. In this review, we firstly introduce the basic definition of chaotic dynamics and review several traditional artificial neuron and neural network models. Then we categorize memristive neuron and neural network models with different biological function mechanisms into five types: memristive autapse neuron, memristive synapse-coupled bi-neuron network, memristive synaptic weight neural network, neuron under electromagnetic radiation, and neural network under electromagnetic radiation. The modeling mechanisms of each type are explained and described in detail. Furthermore, the pioneer works and some recent important papers related to those types are introduced. Finally, some open problems in this field are presented to further explore future work. [ABSTRACT FROM AUTHOR]

Nowadays, there is a lot of study on memristor-based 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. [ABSTRACT FROM AUTHOR]

Locally active memristors with multiple coexisting pinched hysteresis loops have attracted the attention of researchers. However, the currently reported multiple coexisting pinched hysteresis loops memristors are obtained by adding additional piecewise-linear terms into the original Chua corsage memristor. This paper proposes a novel locally active memristor by introducing a polynomial characteristic function into the state equation. The novel memristor has three coexisting pinched hysteresis loops, large relative range of active region and simple emulator circuit. The characteristics of the novel memristor such as power-off plot, coexisting pinched hysteresis loops and DC V – I plot are studied. The memristor is used in a Chua chaotic system to investigate the effects of locally active characteristic on the chaotic oscillation system. Furthermore, the memristor emulator and chaotic system are designed and implemented by commercial circuit elements. The hardware experiments are consistent with numerical simulations. [ABSTRACT FROM AUTHOR]

Biological nonassociative learning is one of the simplest forms of unsupervised learning in animals and can be categorized into habituation and sensitization according to mechanism. This paper proposes a memristive circuit that is based on nonassociative learning and can adapt to repeated inputs, reduce power consumption (habituation), and be sensitive to harmful inputs (sensitization). The circuit includes 1) synapse module, 2) neuron module, 3) feedback module. The first module mainly consists of memristors representing synapse weights that vary with corresponding inputs. Memristance is automatically reduced when a harmful stimulus is input, and climbs at the input interval according to the feedback input when repeated stimuli are input. The second module produces spiking voltage when the total input is above the given threshold. The third module can provide feedback voltage according to the frequency and quantity of input stimuli. Simulation results show that the proposed circuit can generate output signals with biological nonassociative learning characteristics, with varying amplitudes depending on the characteristics of input signals. When the frequency and quantity of the input stimuli are high, the degree of habituation and sensitization intensifies. The proposed circuit has good robustness; can reduce the influence of noise, circuit parasitics and circuit aging during nonassociative learning; and simulate the afterimages caused by visual fatigue for application in automatic exposure compensation. [ABSTRACT FROM AUTHOR]

In this paper, a simple four-wing chaotic attractor is first proposed by replacing the constant parameters of the Chen system with a periodic piecewise function. Then, a new 4D four-wing memristive hyperchaotic system is presented by adding a flux-controlled memristor with linear memductance into the proposed four-wing Chen system. The memristor mathematical structure model is simple and easy to implement. Dynamical analysis and numerical simulation of the memristive hyperchaotic system are carried out. Then, the electronic circuit of the hyperchaotic system is designed and implemented. The results of numerical simulation are in good agreement with the electronic circuit experiment. In addition, shape synchronization control for the 4D four-wing memristive hyperchaotic system is realized, and a communication system is designed by using the shape synchronization method. Finally, secure signal masking application is implemented on Matlab platform. In the developed secure communication scheme, the information signal overlaps with the chaotic masking signal, which improves the security of the system. [ABSTRACT FROM AUTHOR]

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter . At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator. [ABSTRACT FROM AUTHOR]

In this paper, a flux-controlled memristor with linear memductance is proposed. Compared with the memristor with piecewise linear memductance and the memristor with smooth continuous nonlinearity memductance which are widely used in the study of memristive chaotic system, the proposed memristor has simple mathematical model and is easy to implement. Multisim circuit simulation and breadboard experiment are realized, and the memristor can exhibit a pinched hysteresis loop in the voltage-current plane when driven by a periodic voltage. In addition, a new hyper-chaotic system is presented in this paper by adding the proposed memristor into the Lorenz system. The transient chaos and multiple attractors are observed in this memristive system. The dynamical behaviors of the proposed system are analyzed by equilibria, Lyapunov exponents, bifurcation diagram and phase portrait. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a new multi‐wing chaotic attractor is constructed. Based on the proposed multi‐wing system, the paper presents a novel method to generate hyperchaotic multi‐wing attractors. By introducing a flux‐controlled memristor into the proposed multi‐wing system, hyperchaotic multi‐wing attractor is observed in new memristive system. At the same time, the new memristive system has no equilibrium. The phase portraits and Lyapunov exponents are used to analyze the dynamic behaviors of the no‐equilibrium memristive system. Moreover, we analyze the influence on multi‐wing system when adding the memristor in different position. The electronic circuit is realized by using off‐the‐shelf components. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A memristor is the fourth circuit element, which has wide applications in chaos generation. In this paper, a four-dimensional hyperchaotic jerk system based on a memristor is proposed, where the scroll number of the memristive jerk system is controllable. The new system is constructed by introducing one extra flux-controlled memristor into three-dimensional multiscroll jerk system. We can get different scroll attractors by varying the strength of memristor in this system without changing the circuit structure. Such a method for controlling the scroll number without changing the circuit structure is very important in designing the modern circuits and systems. The new memristive jerk system can exhibit a hyperchaotic attractor, which has more complex dynamic behavior. Furthermore, coexisting attractors are observed in the system. Phase portraits, dissipativity, equilibria, Lyapunov exponents and bifurcation diagrams are analyzed. Finally, the circuit implementation is carried out to verify the new system. [ABSTRACT FROM AUTHOR]

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system. [ABSTRACT FROM AUTHOR]

In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage-current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost. [ABSTRACT FROM AUTHOR]

The existing Pavlov associative memory circuit only realizes the simple conditioned reflex process, secondary conditional reflex can make the simple conditioning process more complicated and make the circuit more bionic, but there is a lack of relevant circuit implementation. In this paper, a Pavlov associative memory circuit with secondary conditional reflex is proposed by utilizing the memristor. The proposed circuit can respond to a conditional stimulus after initial learning and have two kinds of forgetting process. Besides, this circuit can indirectly establish conditioned reflexes through conditioned stimuli, instead of directly establishing conditioned reflex with unconditioned stimulus. The realization of secondary conditional reflex is confirmed in the PSPICE simulation results. Meanwhile, an extended classification circuit based on secondary conditioned reflex is proposed. Based on the features of objects as input, the output of the circuit is used to achieve the function of classification. The accuracy of application circuit proposed in this paper can be verified by the simulation results in PSPICE. [ABSTRACT FROM AUTHOR]