Search Results (62)

Despite its significance, hysteresis remains underrepresented in mainstream models of plasticity. In this work, we propose a novel framework that explicitly models hysteresis in simple one- and two-neuron models. Our models capture key feedback-dependent phenomena such as bistability, multistability, periodicity, quasi-periodicity, and chaos, offering a more accurate and general representation of neural adaptation. This opens the door to new insights in computational neuroscience and neuromorphic system design. Synaptic weights change in several contexts or mechanisms including, Bienenstock–Cooper–Munro (BCM) synaptic modification, where synaptic changes depend on the level of post-synaptic activity; homeostatic plasticity, where all of a neuron synapses simultaneously scale up or down to maintain stability; metaplasticity, or plasticity of plasticity; neuromodulation, where neurotransmitters influence synaptic weights; developmental processes, where synaptic connections are actively formed, pruned and refined; disease or injury; for example, neurological conditions can induce maladaptive synaptic changes; spike-time dependent plasticity (STDP), where changes depend on the precise timing of pre- and postsynaptic spikes; and structural plasticity, where changes in dendritic spines and axonal boutons can alter synaptic strength. The ability of synapses and neurons to change in response to activity is fundamental to learning, memory formation, and cognitive adaptation. This paper presents simple continuous and discrete neuro-modules with adapting feedback synapses which in turn are subject to feedback. The dynamics of continuous periodically driven Hopfield neural networks with adapting synapses have been investigated since the 1990s in terms of periodicity and chaotic behaviors. For the first time, one- and two-neuron models are considered as parameters are varied using a feedback mechanism which more accurately represents real-world simulation, as explained earlier. It is shown that these models are history dependent. A simple discrete two-neuron model with adapting feedback synapses is analyzed in terms of stability and bifurcation diagrams are plotted as parameters are increased and decreased. This work has the potential to improve learning algorithms, increase understanding of neural memory formation, and inform neuromorphic engineering research. Full article

The human brain is an extremely sophisticated system. Several neural models have been proposed to mimic and understand brain function. Most of them incorporate memristors to simulate autapse or self-coupling, electromagnetic radiation and the synaptic weight of the neuron. This article introduces and studies the dynamics of a Hopfield neural network (HNN) consisting of four neurons, where one of the synaptic weights of the neuron is replaced by a memristor. Theoretical aspects such as dissipation, the requirements for the existence of attractors, symmetry, equilibrium states and stability are studied. Numerical investigations of the model reveal that it develops very rich and diverse behaviors such as chaos, hyperchaos and transient chaos. These results obtained numerically are further supported by the results obtained from an electronic circuit of the system, constructed and simulated in PSpice. Both approaches show good agreement. In light of the findings from the numerical and experimental studies, it appears that the 4D Hopfield neural network under consideration in this work is more complex than its original version, which did not include a memristor. Full article

This paper is concerned with the event-based synchronization control for chaotic neural networks by using a refined discontinuous trigger scheme. To get rid of the Zeno phenomenon and decrease the triggering times, a refined discontinuous event-trigger (RDET) scheme is employed by designing a new threshold function. The proposed threshold function consists of two parts, i.e., quadratic term and exponential decay term, which makes the derivative of the Lyapunov function possibly not less than zero. On this basis, an important lemma is derived, which contributes to performing a stability analysis. Then, the corresponding closed-loop system model is established in the presence of a trigger scheme. Then, a time-dependent Lyapunov function (TLF) method is established based on the features of an RDET. In view of inequality estimation techniques and stability theory, some synchronization criteria are developed to guarantee that the synchronization of chaotic neural networks can be realized by using the novel discontinuous event-trigger schemes. Finally, a Hopfield neural network is displayed to demonstrate the advantages and effectiveness of the derived results. Full article

This study develops an MTSP model for multi-UAV delivery optimization from a central hub, proposing a hybrid algorithm that integrates genetic simulated annealing-enhanced clustering with an improved Hopfield neural network to minimize the total flight distance. The proposed methodology initially employs an enhanced fuzzy C-means clustering technique integrated with genetic simulated annealing (GSA) to effectively partition the MTSP formulation into multiple discrete traveling salesman problem (TSP) instances. The subsequent phase implements an enhanced Hopfield neural network (HNN) architecture incorporating three key modifications: data normalization procedures, adaptive step-size control mechanisms, and simulated annealing integration, collectively improving the TSP solution quality and computational efficiency. The proposed algorithm’s effectiveness is validated through comprehensive case studies, demonstrating significant performance improvements in the computational efficiency and solution quality compared to conventional methods. The results show that during clustering, the improved clustering algorithm is more stable in its clustering effect. With regard to path optimization, the improved neural network algorithm has a higher computational efficiency and makes it easier to obtain the global optimal solution. Compared with the genetic algorithm and ant colony algorithm, its iteration times, path length, and delivery time are reduced to varying degrees. To sum up, the hybrid optimization algorithm has obvious advantages for solving a multi-UAV collaborative distribution path optimization problem. Full article

This manuscript introduces a simple third-order Hopfield neural network. Its dynamics, implementation with a microcontroller and application to random number generation are explored. The model includes three coupled neurons with no synaptic weights between the first neuron and the third, and between the third and the second. The fundamental features (i.e., symmetry, dissipation and the requirement of existence of an attractor) of the model are studied. The results suggest that the model is asymmetric, dissipative and capable of supporting attractors. The dynamic analysis of the model is conducted through computer explorations, and the findings reveal that it develops complex behaviors like chaos and the coexistence of patterns. The coexistence of patterns is controlled using the linear augmentation method. The coexisting patterns are destroyed, and the multistable system is transformed into a monostable one. In order to confirm the numerical findings, a microcontroller implementation of the considered HNN model is carried out, and the findings of both approaches are concordant. Finally, the elaborated third-order HNN chaotic model is designed for random number generation application. The NIST statistical tests are provided in order to confirm the random features of the generated signals. Full article

The Hopfield Recurrent Neural Network (HRNN) is a single-point descent metaheuristic that uses a single potential solution to explore the search space of optimization problems, whose constraints and objective function are aggregated into a typical energy function. The initial point is usually randomly initialized, then moved by applying operators, characterizing the discrete dynamics of the HRNN, which modify its position or direction. Like all single-point metaheuristics, HRNN has certain drawbacks, such as being more likely to get stuck in local optima or miss global optima due to the use of a single point to explore the search space. Moreover, it is more sensitive to the initial point and operator, which can influence the quality and diversity of solutions. Moreover, it can have difficulty with dynamic or noisy environments, as it can lose track of the optimal region or be misled by random fluctuations. To overcome these shortcomings, this paper introduces a population-based fuzzy version of the HRNN, namely Gaussian Takagi–Sugeno Hopfield Recurrent Neural Network (G-TS-HRNN). For each neuron, the G-TS-HRNN associates an input fuzzy variable of d values, described by an appropriate Gaussian membership function that covers the universe of discourse. To build an instance of G-TS-HRNN(s) of size s, we generate s n-uplets of fuzzy values that present the premise of the Takagi–Sugeno system. The consequents are the differential equations governing the dynamics of the HRNN obtained by replacing each premise fuzzy value with the mean of different Gaussians. The steady points of all the rule premises are aggregated using the fuzzy center of gravity equation, considering the level of activity of each rule. G-TS-HRNN is used to solve the random optimization method based on the support vector model. Compared with HRNN, G-TS-HRNN performs better on well-known data sets. Full article

Memristor-based fractional-order chaotic systems can record information from the past, present, and future, and describe the real world more accurately than integer-order systems. This paper proposes a novel memristor model and verifies its characteristics through the pinched loop (PHL) method. Subsequently, a new fractional-order memristive Hopfield neural network (4D-FOMHNN) is introduced to simulate induced current, accompanied by Caputo’s definition of fractional order. An Adomian decomposition method (ADM) is employed for system solution. By varying the parameters and order of the 4D-FOMHNN, rich dynamic behaviors including transient chaos, chaos, and coexistence attractors are observed using methods such as bifurcation diagrams and Lyapunov exponent analysis. Finally, the proposed FOMHNN system is implemented on a field-programmable gate array (FPGA), and the oscilloscope observation results are consistent with the MATLAB numerical simulation results, which further validate the theoretical analysis of the FOMHNN system and provide a theoretical basis for its application in the field of encryption. Full article

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 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