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.

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.

A large number of studies have shown that astrocytes can be combined with the presynaptic terminals and postsynaptic spines of neurons to constitute a triple synapse via an endocannabinoid retrograde messenger to achieve a self-repair ability in the human brain. Inspired by the biological self-repair mechanism of astrocytes, this work proposes a self-repairing neuron network circuit that utilizes a memristor to simulate changes in neurotransmitters when a set threshold is reached. The proposed circuit simulates an astrocyte-neuron network and comprises the following: 1) a single-astrocyte-neuron circuit module; 2) an astrocyte-neuron network circuit; 3) a module to detect malfunctions; and 4) a neuron PR (release probability of synaptic transmission) enhancement module. When faults occur in a synapse, the neuron module becomes silent or near silent because of the low PR of the synapses. The circuit can detect faults automatically. The damaged neuron can be repaired by enhancing the PR of other healthy neurons, analogous to the biological repair mechanism of astrocytes. This mechanism helps to repair the damaged circuit. A simulation of the circuit revealed the following: 1) as the number of neurons in the circuit increases, the self-repair ability strengthens and 2) as the number of damaged neurons in the astrocyte-neuron network increases, the self-repair ability weakens, and there is a significant degradation in the performance of the circuit. The self-repairing circuit was used for a robot, and it effectively improved the robots' performance and reliability.

The high cost, low yield, and low stability of nanomaterials significantly hinder the application and development of memristors. To promote the application of memristors, researchers proposed a variety of memristor emulators to simulate memristor functions and apply them in various fields. However, these emulators lack nonvolatile characteristics, limiting their scope of application. This article proposes an innovative nonvolatile memristor circuit based on complementary metal–oxide–semiconductor (CMOS) technology, expanding the horizons of memristor emulators. The proposed memristor is fabricated in a reconfigurable array architecture using the standard CMOS process, allowing the connection between memristors to be altered by configuring the on – off state of switches. Compared to nanomaterial memristors, the CMOS nonvolatile memristor circuit proposed in this article offers advantages of low manufacturing cost and easy mass production, which can promote the application of memristors. The application of the reconfigurable array is further studied by constructing an echo state network for short-term load forecasting in the power system.