Hopfield Neural Network Model Research Articles

Advancing urban water-energy demand predictions with a rotor hopfield neural network model optimized by contracted thermal exchange optimizer

ABSTRACT The relationship between urban water and energy demand is crucial for resource efficiency, sustainability, and environmental conservation. Rapid urbanization, population growth, and climate change necessitate integrated models that capture the complex interdependencies, feedback loops, and trade-offs between water and energy systems. This research addresses this intricate relationship by developing a modified Rotor Hopfield Neural Network (RHNN) Model using input indicators like population data, GDP, water consumption, precipitation, electricity consumption, wastewater discharge, and industrial coal usage. The model is optimized using a modified metaheuristic, called Contracted Thermal Exchange Optimizer (CTEO), resulting in a comprehensive forecast of urban water-energy demand. The model’s superior efficiency is demonstrated by comparing it with other contemporary methods. Upon comparison with alternative approaches, it is clear that the RHNN/CTEO model surpasses them, showcasing a mean relative error of 1.47% for water usage and 2.60% for energy consumption. This leads to an overall average MRE of 2.03%. This research contributes to the existing body of knowledge by offering an advanced model for urban water-energy demand forecasting, providing valuable insights for policymakers, urban planners, and stakeholders in making informed decisions related to resource allocation, infrastructure development, and sustainable urban development.

Neural network to solve fuzzy constraint satisfaction problems

<p>It has been proven that solving the constraint satisfaction problem (CSP) is an No Polynomial hard combinatorial optimization problem. This holds true even in cases where the constraints are fuzzy, known as fuzzy constraint satisfaction problems (FCSP). Therefore, the continuous Hopfield neural network model can be utilized to resolve it. The original algorithm was developed by Talaavan in 2005. Many practical problems can be represented as a FCSP. In this paper, we expand on a neural network technique that was initially developed for solving CSP and adapt it to tackle problems that involve at least one fuzzy constraint. To validate the enhanced effectiveness and rapid convergence of our proposed approach, a series of numerical experiments are carried out. The results of these experiments demonstrate the superior performance of the new method. Additionally, the experiments confirm its fast convergence. Specifically, our study focuses on binary instances with ordinary constraints to test the proposed resolution model. The results confirm that both the proposed approaches and the original continuous Hopfield neural network approach exhibit similar performance and robustness in solving ordinary constraint satisfaction problems.</p>

Initial states-induced complex behaviors in a memristive coupled Hopfield neural network model and its application in biomedical image encryption

The multi-stable memristor is a type of memristor that can store multiple conductance states, optimizing information management and improving the efficiency of artificial neural networks such as Hopfield networks. It can improve the performance of Hopfield neural networks by minimizing the synaptic weight between neurons and increasing information storage capacity through its ability to store multiple levels of conductance. This paper presents and discusses a novel Hopfield neural network model composed of two non-identical sub-neural networks coupled by a flux-controlled multi-stable memristor (MCHNN) and its application in biomedical image encryption. Using analysis methods such as bifurcation diagrams, phase portraits, maximum Lyapunov exponent, and basins of attraction, we analyze the dynamics of the MCHNN model associated with coupling strength and initial states. Numerical results show that the proposed MCHNN model is capable of developing rich and complex dynamics, including chaos, double-bubble bifurcations, homogeneous and non-homogeneous coexisting attractors at different positions induced by initial states. To support the numerical results, the MCHNN model is implemented on a ATmega 2560 microcontroller. The results are in very good agreement with those obtained thoeretically and numerically. We exploit the interesting properties of the proposed MCHNN model to generate random bits for biomedical image encryption. We evaluate the robustness and efficiency of the designed image encryption algorithm by carrying out statistical tests and security analyses.

Fractional-order-induced symmetric multi-scroll chaotic attractors and double bubble bifurcations in a memristive coupled Hopfield neural networks

The multi-state memristor is a type of memristor capable of memorizing multiple conductance states. This special feature is successfully used to mimic the behavior of neural synapses and simulate the influences of electromagnetic induction and radiation in artificial neural networks such as Hopfield neural networks. This paper introduces and examines a novel fractional-order Hopfield neural network model consisting of two non-identical sub-Hopfield neural networks coupled by a multi-stable flux controlled memristor (MCFHNN). The pinched hysteresis loops of the multi-stable flux controlled memristor are analyzed via numerical simulations. The equilibrium points of MCFHNN model and their stability are investigated. The introduced MCFHNN model is solved by using Adomian Decomposition Method (ADM). By using some examination methods such as spectral entropy complexity, bifurcation diagrams, phase portraits, maximum Lyapunov exponent and basins of attraction, we analyze the dynamic behaviors of MCFHNN model associated with coupling strength, fractional-order and initial states. Numerical results demonstrate that the proposed MCFHNN model is capable to develop abundant and complicated dynamics including, chaos, multiple transient transition behaviors, double bubble bifurcations, initial-boosted behavior and symmetric multi-scroll chaotic attractors. It is found that the complexity results are in agreement with those obtained from the bifurcation diagrams. This proves that the complexity can well reflect the dynamic behaviors of MCFHNN model. In order to support theoretical and numerical results, the designed MCFHNN model is implemented with the help of an Arduino-Due microcontroller board based on the Atmel SAM3X8E ARM Cortex-M3 processor. The results are in very good agreement with those obtained from computational simulations.

Numerical investigation and deep learning approach for fractal–fractional order dynamics of Hopfield neural network model

This paper investigates the dynamics of Hopfield neural networks involving fractal–fractional derivatives. The incorporation of fractal–fractional derivatives in the neural network framework brings forth novel modeling capabilities, capturing nonlocal dependencies, complex scaling behaviors, and memory effects. The aim of this study is to provide a comprehensive analysis of the dynamics of Hopfield neural networks with fractal–fractional derivatives, including the existence and uniqueness of solutions, stability properties, and numerical analysis techniques. Numerical analysis techniques, including the Adams–Bashforth method, are employed to accurately simulate the fractal–fractional Hopfield neural network system. Moreover, the obtained numerical data serves as validation for developing predictions using Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM) neural network methods. The findings contribute to the advancement of both fractional calculus and neural network theory, providing valuable insights for theoretical investigations and practical applications in complex systems analysis.

Dynamic Analysis and FPGA Implementation of a New Fractional-Order Hopfield Neural Network System under Electromagnetic Radiation.

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.

High-dimensional memristive neural network and its application in commercial data encryption communication

With the development of economic globalization, demands for digital business data sharing among different subsidiary companies are constantly emerging. How to achieve secure transmission of commercial data in the Internet of Things (IoT) is a challenging task. In this paper, we propose a memristive neural network-based method for encrypted communication of commercial data. First, a high-dimensional memristive Hopfield neural network (MMHNN) model with three memristive synapses and seven neurons is proposed and its complex dynamical behaviors are deeply analyzed. The results of theoretical analysis and numerical simulations show that the proposed MMHNN can generate quasi-periodic, periodic, chaotic and hyperchaotic attractors, as well as some controllable 1-direction (1D), 2D, 3D hyperchaotic multi-scroll attractors and other types of parametric regulatory dynamics and initial value regulation dynamics. In addition, an analog equivalent circuit for the MMHNN is constructed, and the circuit simulations experimental results demonstrate the correctness and feasibility of the multi-scroll attractors phenomena. Finally, a novel MMHNN-based encryption scheme for IoT commercial data images is proposed by applying hyperchaotic spatial multi-scroll attractors, and the performance analysis shows that the proposed system achieves good encryption performances, especially in terms of keyspace, information entropy, correlation and differential attacks. The hardware experiments further verify the effectiveness and superiority of the proposed commercial data encryption scheme based on the MMHNN.

Multi-scroll and coexisting attractors in a Hopfield neural network under electromagnetic induction and external stimuli

The application of external stimuli to biological neurons is a valuable tool for investigating neuronal properties, understanding neural circuitry, and developing therapeutic interventions for neurological disorders. In this article, we propose a discrete fractional Hopfield neural network model consisting of four neurons to explore the influence of external stimuli in the presence of electromagnetic induction and radiation. To incorporate the electromagnetic induction between connected neurons, we construct and employ a discrete fractional sine memristor. Additionally, we introduce a multi-level pulse function to the sine memristor element to examine the chaotic dynamics of the neural network model. The qualitative behavior of the network model is demonstrated through stability analysis and bifurcation diagrams showcasing chaos. The study also focuses on understanding the coexisting behavior of the neural network model in the presence and absence of external stimuli. Moreover, we investigate the generation of multi-scroll attractors by varying the level of the pulse function, which is introduced to electromagnetic induction. Numerical simulations reveal that increasing the level of the multi-pulse function doubles the number of scrolls in the attractors when external stimuli are present. The findings presented in this article contribute to our understanding of discrete fractional memristors and shed light on the dynamical behavior of neurons and their electrical activity in the brain. Innovation within the discrete fractional-order Hopfield neural networks realm entails the creation and utilization of fresh ideas, methodologies, and strategies that harness fractional-order dynamics to confront diverse hurdles and enhance the effectiveness of Hopfield networks. Discrete fractional-order Hopfield neural networks have the capacity to propel an array of applications forward, spanning artificial intelligence, machine learning, control systems, and optimization, showcasing their potential for substantial progress in various domains.

Research on the Investment Strategy of Private Equity Investment Fund Targeted Increase in NEEQ — An Empirical Analysis Based on BP and Hopfield Neural Network Model

Private equity investment funds targeted increase in NEEQ has become a new strategy for PE investment. However, the currently adopted Logit regression and one-factor ANOVA models are not suitable for analyzing nonlinear investment activities, and the investment appraisal does not work well. In this paper, all NEEQ companies that implemented private placement in 2017 are used as the study sample. This paper also empirically analyzes the current situation of domestic private equity investment funds based on BP and Hopfield neural network models, then the results of the two models are compared. It is concluded that the accuracy of the BP neural network model can be more than 90%. So, the BP neural network can be used as the optimal model of private equity investment funds investment strategy in NEEQ.

Chaos and firing patterns in a discrete fractional Hopfield neural network model

Chaos and firing patterns in a discrete fractional Hopfield neural network model

A 4D discrete Hopfield neural network-based image encryption scheme with multiple diffusion modes

A novel 4D chaotic map is proposed in this paper using the model of a self-feedback Discrete Hopfield Neural Network (DHNN) with nonlinear synaptic ICMIC (4D-IDHNN). Based on an analysis of chaos characteristics, including attractors, Lyapunov exponents, Bifurcation, Sample Entropy and CO algorithms, the 4D-IDHNN system demonstrates reasonable stochasticity and ergodicity, alongside a broad spectrum of hyperchaotic parameters. Based on the 4D-IDHNN system, we design a new Pixel-dependent bit-plane Chaotic random Diffusion (PbCrD) algorithm with high diffusion capability and security. To begin, the 4D-IDHNN system generates pseudo-random sequences to confuse the plaintext image pixel positions with Chaotic Magic Random Scramble (CMRS). Subsequently, the PbCrD algorithm can be employed to diffuse pixel values. With the initial value of 4D-IDHNN generated using the SHA-256 hash of plaintext image, the ability to resist plaintext attacks can be enhanced. The algorithm includes 24 diffusion modes, which is three times greater than the number of DNA rules, thereby enhancing the complexity of decryption. The proposed encryption algorithm has good effectiveness, robustness, and resistance to differential attacks based on simulations and security analyses.

A novel grid multi-structure chaotic attractor and its application in medical image encryption

Grid multi-scroll/wing chaotic systems are complex non-linear dynamic systems, which are widely used in secure communication. The grid multi-scroll/wing chaotic systems are usually realized by using the function control method, which has a complex realization method, many control parameters, and a simple unit attractor structure. In this paper, based on the Hopfield neural network, a memristive Hopfield neural network model is proposed by using the memristor synapse control method. The model can generate novel grid multi-structure chaotic attractors, which have the characteristics of a simple implementation method, few control parameters, and complex unit attractor structure. Firstly, the generation mechanism of the grid multi-structure chaotic attractors is analyzed by the equilibrium points and stability. Secondly, its basic dynamical characteristics including the Lyapunov exponent spectrum, fractal dimension, time series, power spectrum, bifurcation diagram, and Poincaré section are analyzed. Thirdly, an analog circuit of the neural network model is designed and realized by Multisim. Finally, combined with the chaos encryption principle, an image encryption scheme is designed based on the generated grid multi-structure attractors. Experimental results show that compared with the existing schemes, the proposed scheme has larger information entropy, higher key sensitivity, and a good application prospect.

ASB-CS: Adaptive sparse basis compressive sensing model and its application to medical image encryption

Recent advances in intelligent wearable devices have brought tremendous chances for the development of healthcare monitoring system. However, the data collected by various sensors in it are user-privacy-related information. Once the individuals’ privacy is subjected to attacks, it can potentially cause serious hazards. For this reason, a feasible solution built upon the compression-encryption architecture is proposed. In this scheme, we design an Adaptive Sparse Basis Compressive Sensing (ASB-CS) model by leveraging Singular Value Decomposition (SVD) manipulation, while performing a rigorous proof of its effectiveness. Additionally, incorporating the Parametric Deformed Exponential Rectified Linear Unit (PDE-ReLU) memristor, a new fractional-order Hopfield neural network model is introduced as a pseudo-random number generator for the proposed cryptosystem, which has demonstrated superior properties in many aspects, such as hyperchaotic dynamics and multistability. To be specific, a plain medical image is subjected to the ASB-CS model and bidirectional diffusion manipulation under the guidance of the key-controlled cipher flows to yield the corresponding cipher image without visual semantic features. Ultimately, the simulation results and analysis demonstrate that the proposed scheme is capable of withstanding multiple security attacks and possesses balanced performance in terms of compressibility and robustness.

Landauer Bound and Continuous Phase Transitions.

In this review, we establish a relation between information erasure and continuous phase transitions. The order parameter, which characterizes these transitions, measures the order of the systems. It varies between 0, when the system is completely disordered, and 1, when the system is completely ordered. This ordering process can be seen as information erasure by resetting a certain number of bits to a standard value. The thermodynamic entropy in the partially ordered phase is given by the information-theoretic expression for the generalized Landauer bound in terms of error probability. We will demonstrate this for the Hopfield neural network model of associative memory, where the Landauer bound sets a lower limit for the work associated with 'remembering' rather than 'forgetting'. Using the relation between the Landauer bound and continuous phase transition, we will be able to extend the bound to analog computing systems. In the case of the erasure of an analog variable, the entropy production per degree of freedom is given by the logarithm of the configurational volume measured in units of its minimal quantum.

Analog/digital circuit simplification for Hopfield neural network

Circuit realization of neural networks is a significant approach in neuromorphic computing. Researchers have simplified the circuit for single neuron model, but one for neural network is rarely reported, yet. This paper presents a ReLU-type Hopfield neural network (RHNN) model using simple ReLU function instead of traditional hyperbolic-type function as the activation function. RHNN with three neurons is focused on. Its boundedness and stability are confirmed theoretically, and complex chaotic dynamics are simulated numerically. Further, the printed circuit board (PCB)-based analog circuit is fabricated, and the RHNN circuit has 49.3 % fewer analog components than the Tanh-type HNN circuit. Meanwhile, with logical shift method, an efficient low-cost multiplierless digital circuit is developed on field-programmable gate array (FPGA) platform. Experimental results manifest that resource consumptions of one are less than that of IP core-based digital implementation. Particularly, the RHNN model is well applied to image encryption for satisfying requirements on transmission security.

The dynamics of octonion-valued neutral type high-order Hopfield neural networks with D operator

In this paper, the existence, uniqueness and global exponential stability of pseudo almost periodic solutions for a class of octonion-valued neutral type high-order Hopfield neural network models with D operator are established by using the Banach fixed point theorem and differential inequality techniques. Compared with most existing models, in this class of networks, all connection weights and activation functions are assumed to be octonion-valued functions except for time delays. And unlike most of the existing methods of studying octonion-valued neural networks, our method is a non-decomposition method, that is, the method of directly studying octonion-valued systems. The results and methods in this paper are new. In addition, an example and its numerical simulation are given to illustrate the feasibility of our results.

Research on fire distribution algorithm based on Hopfield neural network

the problem of air defense fire distribution in ECM command and control system is studied. Based on the mathematical model of fire distribution, the classical solution algorithm Hungarian method is introduced, and the shortcomings of Hungarian method in solving fire distribution are pointed out. According to the basic principle of Hopfield neural network model, the algorithm process of solving specific optimization problems is deduced, and the fire distribution problem is simulated. According to the simulation results, the application conclusion and improved method of Hopfield neural network model in fire distribution problem are given, which proves that the model can solve the fire distribution problem more effectively.

English

Rice crop yield prediction suggests the procedure of estimating the rice quantity which is harvested in a provided land region dependent upon several features like farming practices, weather conditions, and soil quality. The main aim of rice crop yield prediction is to offer farmers and agricultural planners correct crop yield calculations in progress, creating informed decisions assuming harvesting, marketing, and planting their crops. It supports farmers in optimizing their production and enhancing their profitability, but also improving food security by ensuring an even supply of rice for consumers. Deep learning (DL) approaches are utilized for predicting crop yield by leveraging the influence of neural networks for learning complex patterns and connections in data. This study presents a Teaching and Learning Based Optimization with Deep Learning for Rice Crop Yield Prediction (TLBODL-RCYP) technique. The proposed TLBODL-RCYP approach emphasizes the accurate forecasting of the rice yield using DL and hyperparameter optimizers. To accomplish this, the TLBODL-RCYP technique performs different preprocessing stages to improve the data quality. Besides, the TLBODL-RCYP technique employs a hybrid Convolution Recurrent HopField Neural Network (HCRHNN) model for yield prediction. At last, the TLBO algorithm was utilized to adjust the hyperparameter values of the HCRHNN technique and thereby enhance the predictive results. The experimental outcome investigation of the TLBODL-RCYP approach is tested with the Kaggle dataset, and the outcomes assured the improvized predictive results of the TLBODL-RCYP method over other recent DL techniques.

Exponential Stability of Hopfield Neural Network Model with Non-Instantaneous Impulsive Effects

We introduce a non-instantaneous impulsive Hopfield neural network model in this paper. Firstly, we prove the existence and uniqueness of an almost periodic solution of this model. Secondly, we prove that the solution of this model is exponentially stable. Finally, we give an example of this model.

ReLU-type Hopfield neural network with analog hardware implementation

Rectified Linear Unit (ReLU) is an extremely simple activation function with two-segment linearity and is usually used in convolutional neural network. To simplify the analog hardware implementation, this article presents a bi-neuron Hopfield neural network (HNN) using ReLU function instead of hyperbolic tangent (Tanh) function as the activation function. With the HNN model, the boundedness properties can be proved by virtue of the Lyapunov method and the stability distributions of time-varying equilibrium point are clarified according to four independent affine regions. Using numerical measures, complex dynamical behaviors are uncovered therein, including period-adding bifurcation, spiking/bursting pattern, fast-slow effect, and coexisting multistable patterns. In addition, a multiplierless electronic circuit is developed for implementing the HNN model and its experimental measurements well validate the numerical ones. The results manifest that the ReLU-type HNN model can display intricate and rich dynamics, and its analog hardware implementation is simpler than other HNN models.