Search Results (91)

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristor-based artificial synapses operate by altering conductance or resistance, making them useful for enhancing the processing capacity and storage capabilities of neural networks. When integrated into systems like Hopfield neural networks, memristors enable the study of complex dynamic behaviors, such as chaos and multistability. Moreover, fractional calculus is significant for their ability to model memory effects, enabling more accurate simulations of complex systems. Fractional-order Hopfield networks, in particular, exhibit chaotic and multistable behaviors not found in integer-order models. By combining memristors with fractional-order Hopfield neural networks, these systems offer the possibility of investigating different dynamic phenomena in artificial neural networks. This study investigates the dynamical behavior of a fractional-order Hopfield neural network (HNN) incorporating a memristor with a piecewise segment function in one of its synapses, highlighting the impact of fractional-order derivatives and memristive synapses on the stability, robustness, and dynamic complexity of the system. Using a network of four neurons as a case study, it is demonstrated that the memristive fractional-order HNN exhibits multistability, coexisting chaotic attractors, and coexisting limit cycles. Through spectral entropy analysis, the regions in the initial condition space that display varying degrees of complexity are mapped, highlighting those areas where the chaotic series approach a pseudo-random sequence of numbers. Finally, the proposed fractional-order memristive HNN is implemented on a Field-Programmable Gate Array (FPGA), demonstrating the feasibility of real-time hardware realization. Full article

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. Full article

The memristor, a revolutionary electronic component, mimics both neural synapses and electromagnetic induction phenomena. Recent study challenges are the development of effective neural models and discovering their dynamics. In this study, we propose a novel Hopfield neural network model leveraging multistable memristors, showcasing its efficacy in encoding biomedical images. We investigate the equilibrium states and dynamic behaviors of our designed model through comprehensive numerical simulations, revealing a rich array of phenomena including periodic orbits, chaotic dynamics, and homogeneous coexisting attractors. The practical realization of our model is achieved using a microcontroller, with experimental results demonstrating strong agreement with theoretical analyses. Furthermore, harnessing the chaos inherent in the neural network, we develop a robust biomedical image encryption technique, validated through rigorous computational performance tests. Full article

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. Full article

The electro-hydraulic servo system has advantages such as high pressure, large flow, and high power, etc., which can also realize stepless regulation, so it is widely used in many engineering machineries. A linear model is sometimes only a simple approximation of an idealized model, but in an actual system, there may be nonlinear and transient variation characteristics in the systems. Coupling is reflected in the fact that the components or functional structures implemented by each system used for the design of hydraulic systems are not completely or independently related to each other, but affect each other. The nonlinear clearance between the actuator and the load reduces the control accuracy of the system and increases the impact, thus losing stable working conditions. In the paper, based on the nonlinear clearance problem of the electro-hydraulic servo system, a mathematical transfer model with clearance is established, and on this basis, a clearance compensation method based on the Hopfield neural network is proposed. In this way, clearance compensation can be realized by adjusting the parameters of neural network nodes, through simple and convenient operation. Finally, by setting different clearance values, the results of the step response and sine response curve before and after clearance compensation of the hydraulic system are compared, and the effectiveness of Hopfield neural network compensation clearance control is verified based on the comparison simulation results. Full article

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological memory. Generative diffusion models are a type of generative machine learning techniques that have shown great performance in many tasks. Similar to associative memory systems, these networks define a dynamical system that converges to a set of target states. In this work, we show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is (asymptotically) identical to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network. Leveraging this connection, we formulate a generalized framework for understanding the formation of long-term memory, where creative generation and memory recall can be seen as parts of a unified continuum. Full article

The primary objective of introducing metaheuristic algorithms into traditional systematic logic is to minimize the cost function. However, there is a lack of research on the impact of introducing metaheuristic algorithms on the cost function under different proportions of positive literals. In order to fill in this gap and improve the efficiency of the metaheuristic algorithm in systematic logic, we proposed a metaheuristic algorithm based on mutation tabu search and embedded it in probabilistic satisfiability logic in discrete Hopfield neural networks. Based on the traditional tabu search algorithm, the mutation operators of the genetic algorithm were combined to improve its global search ability during the learning phase and ensure that the cost function of the systematic logic converged to zero at different proportions of positive literals. Additionally, further optimization was carried out in the retrieval phase to enhance the diversity of solutions. Compared with nine other metaheuristic algorithms and exhaustive search algorithms, the proposed algorithm was superior to other algorithms in terms of time complexity and global convergence, and showed higher efficiency in the search solutions at the binary search space, consolidated the efficiency of systematic logic in the learning phase, and significantly improved the diversity of the global solution in the retrieval phase of systematic logic. Full article

The digital elevation model (DEM) and its derived morphometric factors, i.e., slope, aspect, profile and plan curvatures, and topographic wetness index (TWI), are essential for natural hazard modeling and prediction as they provide critical information about the terrain’s characteristics that can influence the likelihood and severity of natural hazards. Therefore, increasing the accuracy of the DEM and its derived factors plays a critical role. The primary aim of this study is to evaluate and compare the effects of resampling and downscaling the DEM from low to medium resolution and from medium to high resolutions using four methods: namely the Hopfield Neural Network (HNN), Bilinear, Bicubic, and Kriging, on five morphometric factors derived from it. A geospatial database was established, comprising five DEMs with different resolutions: specifically, a SRTM DEM with 30 m resolution, a 20 m resolution DEM derived from topographic maps at a scale of 50,000, a 10 m resolution DEM generated from topographic maps at a scale of 10,000, a 5 m resolution DEM created using surveying points with total stations, and a 5 m resolution DEM constructed through drone photogrammetry. The accuracy of the resampling and downscaling was assessed using Root Mean Square Error (RMSE) and mean absolute error (MAE) as statistical metrics. The results indicate that, in the case of downscaling from low to medium resolution, all four methods—HNN, Bilinear, Bicubic, and Kriging—significantly improve the accuracy of slope, aspect, profile and plan curvatures, and TWI. However, for the case of medium to high resolutions, further investigations are needed as the improvement in accuracy observed in the DEMs does not necessarily translate to the improvement of the second derivative morphometric factors such as plan and profile curvatures and TWI. While RMSEs of the first derivatives of DEMs, such as slope and aspect, reduced in a range of 8% to 55% in all five datasets, the RMSEs of curvatures and TWI slightly increased in cases of downscaling and resampling of Dataset 4. Among the four methods, the HNN method provides the highest accuracy, followed by the bicubic method. The statistics showed that in all five cases of the experiment, the HNN downscaling reduced the RMSE and MAE by 55% for the best case and 10% for the worst case for slope, and it reduced the RMSE by 50% for the best case of aspect. Both the HNN and the bicubic methods outperform the Kriging and bilinear methods. Therefore, we highly recommend using the HNN method for downscaling DEMs to produce more accurate morphometric factors, slope, aspect, profile and plan curvatures, and TWI. Full article

The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated. Full article

Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis. Full article

Studying the firing dynamics and phase synchronization behavior of heterogeneous coupled networks helps us understand the mechanism of human brain activity. In this study, we propose a novel small heterogeneous coupled network in which the 2D Hopfield neural network (HNN) and the 2D Hindmarsh–Rose (HR) neuron are coupled through a locally active memristor. The simulation results show that the network exhibits complex dynamic behavior and is different from the usual phase synchronization. More specifically, the membrane potential of the 2D HR neuron exhibits five stable firing modes as the coupling parameter $k_1$ changes. In addition, it is found that in the local region of $k_1$, the number of spikes in bursting firing increases with the increase in $k_1$. More interestingly, the network gradually changes from synchronous to asynchronous during the increase in the coupling parameter $k_1$ but suddenly becomes synchronous around the coupling parameter $k_1$ = 1.96. As far as we know, this abnormal synchronization behavior is different from the existing findings. This research is inspired by the fact that the episodic synchronous abnormal firing of excitatory neurons in the hippocampus of the brain can lead to diseases such as epilepsy. This helps us further understand the mechanism of brain activity and build bionic systems. Finally, we design the simulation circuit of the network and implement it on an STM32 microcontroller. Full article

In this study a four-wheel independent steering (4WIS) system for an electric vehicle (EV) steered by stepper motors is presented as a revolutionary real-time control technique employing neural networks in combination with fuzzy logic, where the use of the neural network greatly simplifies the computational process of fuzzy logic. The control of the four wheels is based on a variation of a Hopfield Neural Network (VHNN) method, in which the input is the error of each steering motor and the output is processed by a hyperbolic tangent function (HTF) feeding the fuzzy logic controller (FLC), which ultimately drives the stepper motor. The whole system consists of the four aforementioned blocks which work in sync and are inseparable from each other with the common goal of driving all the steering stepper motors at the same time. The novelty of this system is that each wheel monitors the condition of the others, so even in the case of the failure of one wheel, the vehicle does not veer off course. The results of the simulation show that the suggested control system is very resilient and workable at all angles and speeds. Full article

This paper presents a study on a memristive two-neuron-based Hopfield neural network with fractional-order derivatives. The equilibrium points of the system are identified, and their stability is analyzed. Bifurcation diagrams are obtained by varying the magnetic induction strength and the fractional-order derivative, revealing significant changes in the system dynamics. It is observed that lower fractional orders result in an extended bistability region. Also, chaos is only observed for larger magnetic strengths and fractional orders. Additionally, the application of the fractional-order model for image encryption is explored. The results demonstrate that the encryption based on the fractional model is efficient with high key sensitivity. It leads to an encrypted image with high entropy, neglectable correlation coefficient, and uniform distribution. Furthermore, the encryption system shows resistance to differential attacks, cropping attacks, and noise pollution. The Peak Signal-to-Noise Ratio (PSNR) calculations indicate that using a fractional derivative yields a higher PSNR compared to an integer derivative. Full article

In response to the COVID-19 pandemic, communities utilize unmanned vehicles to minimize person-to-person contact and lower the risk of infection. This paper addresses the critical considerations of these unmanned vehicles’ maximum load capacity and service time, formulating them as constraints within a multi-traveling salesman problem (MTSP). We propose a comprehensive optimization approach that combines a genetic simulated annealing algorithm with clustering techniques and an improved Hopfield neural network (IHNN). First, the MTSP is decomposed into multiple independent TSPs using the fuzzy C-means clustering algorithm based on a genetic simulated annealing algorithm (SA-GA-FCM). Subsequently, the HNN is employed to introduce the data transformation technique and dynamic step factor to prepare more suitable inputs for the HNN training process to avoid the energy function from falling into local solutions, and the simulated annealing algorithm is introduced to solve multiple TSP separately. Finally, the effectiveness of the proposed algorithm is verified by small-scale and large-scale instances, and the results clearly demonstrate that each unmanned vehicle can meet the specified constraints and successfully complete all delivery tasks. Furthermore, to gauge the performance of our algorithm, we conducted ten simulation comparisons with other combinatorial optimization and heuristic algorithms. These comparisons indicate that IHNN outperforms the algorithms mentioned above regarding solution quality and efficiency and exhibits robustness against falling into local solutions. As presented in this paper, the solution to the unmanned vehicle traveling salesman problem facilitates contactless material distribution, reducing time and resource wastage while enhancing the efficiency of unmanned vehicle operations, which has profound implications for promoting low-carbon sustainable development, optimizing logistics efficiency, and mitigating the risk of pandemic spread. Full article

With the development of data collection and storage capabilities in recent decades, abundant data have been accumulated in geotechnical engineering fields, providing opportunities for the usage of machine learning approaches. Thus, a rising number of scholars are adopting machine learning techniques to settle geotechnical issues. In this paper, the application of three popular machine learning algorithms, support vector machine (SVM), artificial neural network (ANN), and decision tree (DT), as well as other representative algorithms in geotechnical engineering, is reviewed. Meanwhile, the applicability of diverse machine learning algorithms in settling specific geotechnical engineering issues is compared. The main findings are as follows: ANN, SVM, and DT have been widely adopted to solve a variety of geotechnical engineering issues, such as the classification of soil and rock types, predicting the properties of geotechnical materials, etc. Based on the collected relevant research, the performance of random forest (RF) in sorting soil types and assessing landslide susceptibility is satisfying; SVM has high precision in classifying rock types and forecasting rock deformation; and backpropagation ANNs and Hopfield ANNs are recommended to forecast rock compressive strength and soil settlement, respectively. Full article