The secure transmission of images in critical applications like smart healthcare and autonomous driving demands encryption schemes that are both highly secure and efficient. While chaos-based systems are promising, their security is fundamentally limited by the complexity of the underlying chaotic generator. This paper introduces a novel complex-valued discrete-time Hopfield neural network (CVDHNN) to address this challenge. We demonstrate that the CVDHNN exhibits rich hyperchaotic dynamics through various numerical analyses. The network is successfully implemented on an FPGA, verifying its capability for chaotic sequence generation. Leveraging this complex chaos, we design a robust image encryption algorithm that integrates multi-stage confusion and diffusion. Security analysis confirms the cipher’s excellence, achieving favorable statistical properties, high key sensitivity, and strong resistance to various attacks.

Memristors with nonlinearity and memory characteristics can effectively enhance chaotic dynamics complexity for chaotic maps. In this work, we present a novel discrete memristor model and couple it with sine maps and iterative chaotic maps with infinite collapse (ICMIC) to construct a class of discrete memristive hyperchaotic maps with multicavity multistructure attractors. This class of multicavity multistructure memristive sine ICMIC modulation maps (MCMS-MSIMMs) possesses an infinite variety of configurations, where the quantity and position of coupled discrete memristors can be arbitrarily combined. Numerical simulation results demonstrate that the sample map can exhibit hyperchaos, nondegeneracy, large-scale parameter control, multicavity attractors, multistructure attractors, and multicavity multistructure attractors. The complexity and initial values of the system are explored, revealing the high permutation entropy and initial offset-boosting behavior. In addition, the field programmable gate array (FPGA)-based MCMS-MSIMM hardware circuit is designed, and the experimental results are consistent with the numerical results. Finally, MCMS-MSIMM is applied in secure communication, and the experimental results indicate that the proposed map has better noise resistance performance compared to existing maps.

Nowadays, while enjoying the convenience brought by the Internet of Things (IoT), people are also facing significant challenges in information security. A stable and reliable random source is an indispensable component of IoT secure communication system. This paper explores the dynamics in a discrete neuron map influenced by the memristive delay feedback. The investigation considers feedback strength, delay length, and initial conditions as key parameters, and employs numerical analyses including phase diagrams, Lyapunov exponents, bifurcation diagrams, and Kaplan-Yorke dimensions, to explore the diverse dynamical behaviors of the discrete memristive delay feedback neuron model. The study uncovers an inherent connection between the complexity of the dynamic behavior and the control parameters, as well as the delay length. Further exploration into initial condition-dependent dynamics reveals the intricate coexistence of homogeneous and heterogeneous attractors. Furthermore, the proposed model is successfully implemented on an FPGA platform, with experimental results validating its feasibility and effectiveness, contributing to a deeper understanding of delay effects in discrete memristive neural systems. Moreover, the secure communication system is designed based on the memristive delay feedback neuron model. The performance against noise is evaluated through numerical simulations demonstrating its effectiveness in secure communication.

Most existing visual object tracking (VOT) approaches are implemented based on the von Neumann computation systems, which inevitably have the problems of high latency. Additionally, remote server processing of video resources requires a large amount of data transmission over the Internet, which limits real-time tracking performance. The integration of VOT technology into electronic devices has become a new trend. However, current VOT approaches have high algorithm complexity, making it difficult to design the circuits to implement the corresponding functions. In this article, a memristor-based attention network (MAN) and its corresponding algorithm are proposed to achieve online real-time tracking under parallel computing. Memristors are used to construct the attention encoding circuits to record changes of the target in historical frames, and adjust attention signals to the target online and in real-time during the tracking process, avoiding the latency problem of the von Neumann architecture. Inspired by the working process of$\gamma $-GABAergic interneuron and tripartite synapse, we propose an attention allocation module to selectively allocate attention values. Combining the winner-take-all principle, we design a target localization circuit and an optimal attention zone selection circuit for the parallel computation to track the location of the target. Finally, the experiments and analyses on the OTB-100, NFS, and VOT-RTb2022 benchmark datasets verify that the proposed MAN has promising tracking performance and achieves a tracking speed of 1000 frames per second, demonstrating superior real-time performance.

The brain emotional learning network offers several advantages when compared to traditional neural networks. It features a simpler structure, low computational complexity, and fast training speed. These characteristics make it ideal for applications like pattern recognition, data classification, and intelligent control. However, current brain emotional learning networks, including their modified networks, are not capable of recognizing or classifying data in complex environments. To address this issue, this paper proposes a brain emotional learning network with an attention mechanism that strengthens the processing of key information while suppressing interfering information, thereby enabling the network to recognize data within complex environments. Furthermore, software implementation of neural networks often experiences slow computing speeds due to the separation of storage and computation in traditional von Neumann computers. To combat this issue, the paper presents a hardware circuit implementation of the attention mechanism-based brain emotional learning network using memristors. Finally, the designed in-memory computing neural network has been successfully applied to the recognition of traffic signs within complex environments, and has achieved accurate and rapid recognition.

Memristors, with their unique nonlinear characteristics, are highly suitable for construction novel neural models with rich dynamic behaviors. In this paper, a memristor with piecewise nonlinear state function is introduced into the tabu learning neuron model, resulting in a novel memristive tabu learning neuron model capable of generating a double-wing chaotic butterfly. By modulating the state function of the memristor, we can effectively and easily alter the number of wings of the chaotic butterfly. Equilibrium points analysis further elucidates the mechanism behind the generation of multi-wing chaos. Various numerical simulation techniques, including phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and local attraction basins, are employed to illustrate the dynamical behaviors of the proposed model. Moreover, the newly constructed neuron model is validated using FPGA hardware, with the results aligning with numerical simulations, thereby offering a dependable foundation for a memristor digital circuit-based brain-like neuron model. Lastly, an image encryption application based on the multi-wing chaotic butterfly is developed to demonstrate the potential application of the model.

The delay of state variable plays a crucial role in chaotic systems. However, it has not received sufficient attention in discrete memristor-based maps. This paper presents a study on the effects of delay feedback in the discrete memristive system, proposing a generalized delay difference feedback memristive map. The dynamical behaviors influenced by control parameters, delay length and initial conditions, are explored through four discrete memristive maps. The Kaplan-Yorke dimension is utilized as an indicator to investigate the chaotic dynamic variations induced by the delay length within memristive maps. Furthermore, digital circuits for the proposed systems are designed and implemented, with hardware experimental results that are consistent with numerical simulations, thereby verifying the effectiveness of the digital circuit-based system and providing a foundation for hardware-based delay difference system design. Additionally, the chaotic series are integrated into the particle swarm optimization for tackling obstacle avoidance path planning. The superiority of the designed delay difference feedback memristive maps is highlighted through comparisons with several classical chaotic maps, showcasing their enhanced performance in terms of the speed and cost efficiency in solving the path planning task.

The randomness of chaotic systems are crucial for their application in secure communication. Conservative systems exhibit enhanced ergodicity and randomness in comparison to dissipative chaotic systems. However, the memristor-based conservative chaotic maps remain unreported. This article presents a study of volume-preserving chaotic maps based on discrete memristor (DM). We propose and analyze a generic conservative map that incorporates DM. The conservative characteristics of the proposed iterative map are confirmed through the determinant of its Jacobian matrix. Furthermore, four distinct DM models are introduced and their memristive characteristics are verified through numerical simulations of hysteresis loops. To investigate the dynamical properties of the discrete memristive conservative map (DMCM), we incorporate the proposed DM models into the generic conservative map model using numerical methods, including phase portraits, Lyapunov exponents, and bifurcation diagrams. Additionally, the hardware implementation of the DMCM on an FPGA platform demonstrates the reliability of the model. Finally, secure communication experiments based on the DMCM show that it outperforms some classical dissipative chaotic maps in terms of bit error rate performance.

Memristive neuromorphic networks have great potential and advantage in both technology and computational protocols for artificial intelligence. Efficient hardware design of biological neuron models forms the core of research problems in neuromorphic networks. However, most of the existing research has been based on logic or integrated circuit principles, limited to replicating simple integrate-and-fire behaviors, while more complex firing characteristics have relied on the inherent properties of the devices themselves, without support from biological principles. This paper proposes a memristor-based neuron circuit system (MNCS) according to the microdynamics of neurons and complex neural cell structures. It leverages the nonlinearity and non-volatile characteristics of memristors to simulate the biological functions of various ion channels. It is designed based on the Hodgkin-Huxley (HH) model circuit, and the parameters are adjusted according to each neuronal firing mechanism. Both PSpice simulations and practical experiments have demonstrated that MNCS can replicate 24 types of repeating biological neuronal behaviors. Furthermore, the results from the Joint Inter-spike Interval(JISI) experiment indicate that as the background noise increases, MNCS exhibits pulse emission characteristics similar to those of biological neurons.

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 theon–offstate 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.

To overcome the energy efficiency bottleneck of the von Neumann architecture and scaling limit of silicon transistors, an emerging but promising solution is neuromorphic computing, a new computing paradigm inspired by how biological neural networks handle the massive amount of information in a parallel and efficient way. Recently, there is a surge of interest in the nematode worm Caenorhabditis elegans (C. elegans), an ideal model organism to probe the mechanisms of biological neural networks. In this article, we propose a neuron model for C. elegans with leaky integrate-and-fire (LIF) dynamics and adjustable integration time. We utilize these neurons to build the C. elegans neural network according to their neural physiology, which comprises: 1) sensory modules; 2) interneuron modules; and 3) motoneuron modules. Leveraging these block designs, we develop a serpentine robot system, which mimics the locomotion behavior of C. elegans upon external stimulus. Moreover, experimental results of C. elegans neurons presented in this article reveals the robustness (1% error w.r.t. 10% random noise) and flexibility of our design in term of parameter setting. The work paves the way for future intelligent systems by mimicking the C. elegans neural system.

Spiking neural networks (SNNs) are biologically plausible and computationally powerful. The current computing systems based on the von Neumann architecture are almost the hardware basis for the implementation of SNNs. However, performance bottlenecks in computing speed, cost, and energy consumption hinder the hardware development of SNNs. Therefore, efficient non von Neumann hardware computing systems for SNNs remain to be explored. In this article, a selective supervised algorithm for spiking neurons (SNs) inspired by the selective attention mechanism is proposed, and a memristive SN circuit as well as a memristive SNN circuit based on the proposed algorithm are designed. The memristor realizes the learning and memory of the synaptic weight. The proposed algorithm includes a top-down (TD) selective supervision method and a bottom-up (BU) selective supervision method. Compared with other supervised algorithms, the proposed algorithm has excellent performance on sequence learning. Moreover, TD and BU attention encoding circuits are designed to provide the hardware foundation for encoding external stimuli into TD and BU attention spikes, respectively. The proposed memristive SNN circuit can perform classification on the MNIST dataset and the Fashion-MNIST dataset with superior accuracy after learning a small number of labeled samples, which greatly reduces the cost of manual annotation and improves the supervised learning efficiency of the memristive SNN circuit.

Due to the synapse-like nonlinearity and memory characteristics, memristor is often used to construct memristive neural networks with complex dynamical behaviors. However, memristive neural networks with multistructure chaotic attractors have not been found yet. In this article, a novel method for designing multistructure chaotic attractors in memristive neural networks is proposed. By utilizing a multipiecewise memristive synapse control in a Hopfield neural network (HNN), various complex multistructure chaotic attractors can be produced. Theoretical analysis and numerical simulation demonstrate that multiple multistructure chaotic attractors with different topologies can be generated by conducting the memristive synapse-control in different synaptic coupling positions. Differing from traditional multiscroll attractors, the generated multistructure attractors contain multiple irregular shapes instead of simple scrolls. Meanwhile, the number of structures can be easily controlled with the memristor control parameters. Furthermore, we design a module-based analog memristive neural network circuit and the arbitrary number of multistructure attractors can be obtained by selecting corresponding control voltages. Finally, based on the memristive HNNs, a novel image encryption cryptosystem with a permutation-diffusion structure is designed and evaluated, exhibiting its excellent encryption performances, especially the extremely high key sensitivity.

Memristors have recently demonstrated great promise in constructing memristive neural networks with complex dynamics. This article 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 multistructure 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 multistructure 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 multistructure attractors as well as the space coexisting attractors are experimentally demonstrated. Finally, we design a pseudorandom number generator to explore the potential application of the proposed TM-HNN.

Emotional intelligence plays an important role in artificial intelligence. The brain circuitry of emotion mainly includes the prefrontal cortex, the amygdala, hippocampus andet 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.

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.

Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are core components in the field of signal processing. However, in the existing research, there is no fully analog circuit that can realize the one-step calculation of FFT. Therefore, in this paper, an analog circuit that can calculate FFT and its inverse transform IFFT in one-step is proposed. First, a circuit that can realize complex number operations is designed. On the basis of this structure, a fully analog circuit that can realize fast and efficient computing of FFT and IFFT in one-step is proposed. In addition, different coefficient matching can be obtained to achieve arbitrary points of FFT and IFFT by adjusting the resistance value of the memristor, which has good programmability. Specific examples are given in the paper to evaluate the proposed method. The PSPICE simulation results show that the average accuracy is above 99.98%. More importantly, the calculation speed has been greatly improved compared with MATLAB simulation. Finally, the proposed circuit can be used to quickly solve convolution operation, and the average accuracy can reach 99.95%.

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.

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.

Currently, some works on studying complete synchronization of dynamical systems are usually restricted to its two special cases: 1) power-rate synchronization and 2) exponential synchronization. Therefore, how to give a generalization of these types of complete synchronization by the mathematical expression is an open question that needs to be urgently solved. To begin with, this article proposes multimode function synchronization by the mathematical expression for the first time, which is a generalization of exponential synchronization, power-rate synchronization, logarithmical synchronization, and so on. Moreover, two adaptive controllers are designed to achieve robust multimode function synchronization of memristive neural networks (MNNs) with mismatched parameters and uncertain parameters. Each adaptive controller includes function$r(t)$and update gain$\sigma $. By choosing different types of$r(t)$, multiple types of complete synchronization, including power-rate synchronization and exponential synchronization can be obtained. And update gain$\sigma $can be used to adjust the speed of synchronization. Therefore, our results enlarge and strengthen the existing results. Two examples are put forward to verify the validity of our results.

In this paper, we propose a hyperchaotic image encryption system based on particle swarm optimization algorithm (PSO) and cellular automata (CA). Firstly, to improve the ability to resist plaintext attacks, the initial conditions of the hyperchaotic system are generated by the hash function value which is closely related to the plaintext image to be encrypted. In addition, the fitness of PSO is the correlation coefficient between adjacent pixels of the image. Moreover, On the basis of hyperchaotic system, cellular automata technology is adopted, which can enhance the randomness of population distribution and increase the complexity and diversity of the population so that the security of the encryption system can be improved and avoid falling into local optimum. The simulation results and security analysis of the proposed encryption system demonstrate that the hyperchaotic image encryption system has high resistance against plaintext attack and statistical attack.

Inhomogeneous linear ordinary differential equations (ODEs) and systems of ODEs can be solved in a variety of ways. However, hardware circuits that can perform the efficient analog computation to solve them are rarely in the literature. To address such problems, this paper proposes a general method of using a memristor-capacitor (M-C) circuit to solve inhomogeneous linear ODEs and systems of ODEs of any order in initial value problems. The M-C circuit can match the coefficients of the equations sought by adjusting the memristor resistance value according to the coefficient formula proposed in the paper, which has higher programmability. Then, some ODEs and systems of ODEs are given in the paper as examples to evaluate the proposed method. According to the comparison results based on MATLAB software simulation and the simulation based on OrCAD software, the designed M-C circuit has an effective improvement in speed and the accuracy exceeds 99.95% in software simulation. Based on practical verification, this paper gives the actual M-C circuit experiment based on PCB. Moreover, the proposed method can be used to quickly solve the object motion state in the spring mass damping system in actual engineering, and the accuracy can reach 99.98%.

Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.

It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.

In this paper, cluster synchronization on multiple nonlinearly coupled dynamical subnetworks of complex networks with nonidentical nodes and stochastic perturbations is studied. Based on the general leader-follower's model, an improved network structure model that consists of multiple pairs of matching subnetworks, each of which includes a leaders' subnetwork and a followers' subnetwork, is proposed. Moreover, the dynamical behaviors of the nodes belonging to the same pair of matching subnetworks are identical, while the ones belonging to different pairs of unmatched subnetworks are nonidentical. In this new setting, the aim is to design some suitable adaptive pinning controllers on the chosen nodes of each followers' subnetwork, such that the nodes in each subnetwork can be exponentially synchronized onto their reference state. Then, some cluster synchronization criteria for multiple nonlinearly coupled dynamical subnetworks of complex networks are established, and a pinning control scheme that the nodes with very large or low degrees are good candidates for applying pinning controllers is presented. Suitable adaptive update laws are used to deal with the unknown feedback gains between the pinned nodes and their leaders. Finally, several numerical simulations are given to demonstrate the effectiveness and applicability of the proposed approach.