Due to the fixed weights and simple topology of traditional unidirectional ring neural networks, it is challenging to generate complex firing dynamics. This paper introduces two threshold memristor models to mimic neuronal autapses, constructing a novel dual memristor-coupled unidirectional ring neural network (DMCURNN). Benefiting from the dual memristor-based autapse emulation, the DMCURNN enriches diverse hidden firing dynamics that are absent in conventional unidirectional ring neural networks, and the richness and complexity of these hidden firing dynamics are highly sensitive to the memristive coupling strengths. Numerical simulations indicate that the DMCURNN is able to generate various hidden firing activities, pattern transitions, homogeneous firing multistability of infinite coexisting homogeneous firing patterns and heterogeneous firing multistability of seven heterogeneous firing patterns. Furthermore, through adjusting the coupling parameters along with the external current intensity, the regulatory mechanisms of hidden firing patterns and their amplitude and frequency regulation are revealed. Subsequently, the hidden firing dynamics of this network are verified on an FPGA hardware platform. Finally, Using the hidden firing multistability characteristic of the DMCURNN, a novel bitstream-based hardware image encryption scheme with a dynamic key update mechanism is designed. Performance evaluations demonstrate that the proposed scheme exhibits exceptional robustness and high efficiency for IoT security applications.

Memristors possess unique characteristics, including nano-scale dimensions, non-volatility, programmability and synaptic plasticity, enabling them to simulate biological neuronal synapses. Despite existing memristor-synaptic coupled neuron models demonstrating diverse firing patterns under varying initial conditions, the diversity of their multistable firing behaviors remains limited. To address this issue, a new multistable ReLU-type memristor with a piecewise linear function is proposed to couple FitzHugh–Nagumo (FHN) and Hindmarsh–Rose (HR) neurons, establishing a novel multistable ReLU-type memristive heterogeneous neuron model (MRMHNM). Numerical calculations indicate that this MRMHNM displays rich firing dynamics, including periodic spiking firing, chaotic bursting firing, and multi-scroll firing with adjustable scroll numbers. Significantly, it demonstrates distinct firing multistability, encompassing the homogeneous multistability of initial offset-boosted coexisting single-scroll firings, as well as peculiar behaviors in both homogeneous and heterogeneous coexisting scenarios, where the amount of the heterogeneous and homogeneous firings can theoretically increase without bound. In addition, pattern transitions, phase synchronization and geometrically controllable firing behaviors are also comprehensively revealed and investigated. Moreover, a digital hardware platform based on the STM32 microcontroller is employed to implement and verify these intriguing discoveries. Lastly, using the distinctive multistability and multi-scroll firing dynamics of the MRMHNM, a new image secure communication system is built, and experimental results confirm its excellent reliability and security performance.

In this paper, by taking a locally active memristor (LAM) as the neuronal synapse to link two identical/disparate ReLU-type Hopfield neural networks (RHNNs), the memristive homogeneous and heterogeneous neural networks are presented and their coupling dynamics are discussed in succession. The homogeneous RHNN model consists of two 3D RHNNs with a LAM, in which the coupling strength-and initial value-induced synchronous transitions are revealed. Besides, the heterogeneous RHNN model is focused on which is constructed by using a LAM to couple a 3D and 2D RHNN, where complex and rich dynamics are revealed in numerical, including hyperchaos, chaos, quasi-period, and multi-stable patterns. Particularly, attractor control of offset boosting as well as color image encryption application are realized, indicating the high controllability and security of the LAM-coupled neural networks. Finally, the electrical neuron depending on the digital circuit is implemented and hardware experimental results verify the numerical measurements well.

Owing to their ability to effectively characterize the memory effect of magnetic flux, specifically in relation to the effect of external electromagnetic radiation, memristors have elicited widespread interest in the construction of neural networks with complex dynamics. This work proposes a novel memristive multiscroll multistable neural network (MMSMSNN), wherein multistable threshold memristors are used to describe external electromagnetic radiation effects. Numerical simulations show that the MMSMSNN can yield any number of cubic lattice multiscroll attractors by adjusting the internal parameters of memristors. Another highlight is that it can also be able to yield abundant initial offset boosting behaviors, i.e., different kinds of infinitely many homogeneous coexisting attractors, including linearly arranged homogeneous coexisting attractors, planar lattice-distributed homogeneous coexisting attractors, and cubic lattice-distributed homogeneous coexisting attractors. In addition, hardware experiments based on the CH32V307 microcontroller are carried out to demonstrate the numerical findings. Finally, a new secure medical image communication scheme is designed to investigate the MMSMSNN in practical applications, and performance analyses reveal its superiority and high security.

When using a synapse as a coupler to connect neurons, parameter-based synchronization transitions have been investigated. However, the dependence on initial conditions has not been comprehensively discussed in the literature. This work presents an electrical-synapse-coupled model consisting of two homogeneous Hopfield neural networks (HNNs), which is the simplest network-to-network coupling model known for HNN. The model possesses several fixed points, which are found to be unstable. Simulation results of peak differences, bifurcation diagrams, and normalized mean synchronization errors indicate that complex synchronization transitions occur, depending on both the electrical coupling strength and initial conditions. Particularly, we focus here on mapping the basins of attraction between periodic and chaotic synchronization for bistable patterns. Finally, a multiplierless electrical neuron circuit is developed to validate initial condition-induced synchronization phenomena, which provides a new perspective for the study of collective dynamics of brain-like networks and the development of lightweight neuromorphic circuits.

Thanks to the biomimetic properties of synaptic plasticity, memristors are often utilized to mimic biological neuronal synapses. This article presents a new memristor synapse coupling (MSC) approach for producing multidirectional multidouble-scroll attractors. Through adopting flux-controlled hyperbolic memristor synapses to couple a Hopfield neural network, a novel multidirectional multidouble-scroll Hopfield neural network (MDMDSHNN) is constructed. Theoretical results and numerical calculations indicate that MDMDSHNN is capable of producing any desired amount of multidirectional multidouble-scroll attractors, including unidirectional (1-D), bidirectional (2-D), and three-directional (3-D) multidouble-scroll attractors. Furthermore, an infinite amount of initial offset-boosted coexisting multidouble-scroll chaotic attractors possessing identical shapes but different positions, i.e., homogeneous extreme multistability are also found via switching the memristor initial values. Furthermore, to validate the physical implementability and practicality of MDMDSHNN, the digital hardware platform is performed. Finally, to investigate MDMDSHNN in practical application, an image encryption scheme with superior security performance is given by employing the homogeneous multidouble-scroll chaotic sequences, further illustrating good superiority and effectiveness of the present MSC method.

Aligning software product versions to commits is extremely important for fixing vulnerabilities in released versions. Existing work is proposed based on tags in the code repository. However, in practice, many software versions widely used in IT companies are reported with many high-risk vulnerabilities. In contrast, they have no indicator information (i.e., tags) in their source code repository. Such a situation results in the difficulty of tracing special versions to their particular commits for effectively fixing vulnerabilities. In this paper, we first study the software released on the Maven repository and hosted on GitHub. We collect and analyze the statistics of those versions that are reported with high-risk vulnerabilities but have no explicit information to locate the commit where they are released. To effectively locate the commits where a special version is released, we propose a novel approach named ContAlign and make a comprehensive comparison with three baselines that are proposed based on the two most common strategies: time-based ones and range-based ones. The experimental results on our built dataset indicate that ContAlign can obtain a good performance of 0.89 in terms of accuracy when identifying the commit range which covers the truth release commit of a specific version and improves baselines by 50.3%-102.20/0. Besides, we also conduct a human study with 10 participants to evaluate the performance and usefulness of ContAlign, the user feedback indicates that ContAlign can effectively help participants align vulnerability versions to commits to the code repository.

Detection of hidden dynamics is of great value in model prediction and control engineering. To explore its effects and control methods in the memristive network model, this paper presents a memristor synapse-driven ReLU-type Hopfield neural network (MRHNN). The generalized Hamilton function is derived from Helmholtz’s theorem and the equilibrium points of the model are analyzed. It is found via numerical computations that because of no existence of equilibrium, the MRHNN model always unfolds hidden dynamics, including hidden bifurcation, hidden mode transition, hidden transient chaos, and hidden multistability. In addition, amplitude and offset boosting control of hidden attractors are executed, illustrating the flexibility of the attractor regulation. Finally, based on digital hardware devices, circuit experiments are deployed and their measurements well agree with the numerical results, certifying the dynamical effects and lossless control of the memristive neural network and physical reliability of the electronic neuron.

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.