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We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show that this type of learning can lead to prototype formation, where unlearned states emerge as representatives of large correlated subsets of states, alleviating capacity woes. This process has similarities to prototype learning in human cognition. We provide a substantial literature review of prototype learning in associative memories, covering contributions from psychology, statistical physics, and computer science. We analyze prototype formation from a theoretical perspective and derive a stability condition for these states based on the number of examples of the prototype presented for learning, the noise in those examples, and the number of nonexample states presented. The stability condition is used to construct a probability of stability for a prototype state as the factors of stability change. We also note similarities to traditional network analysis, allowing us to find a prototype capacity. We corroborate these expectations of prototype formation with experiments using a simple Hopfield network with standard Hebbian learning. We extend our experiments to a Hopfield network trained on data with multiple prototypes and find the network is capable of stabilizing multiple prototypes concurrently. We measure the basins of attraction of the multiple prototype states, finding attractor strength grows with the number of examples and the agreement of examples. We link the stability and dominance of prototype states to the energy profile of these states, particularly when comparing the profile shape to target states or other spurious states. [ABSTRACT FROM AUTHOR]

Nowadays, unmanned aerial vehicles (UAVs) becomes more prominent because of their benefits namely versatile, inexpensive, scalable, and autonomous. The aerial image classification procedure has involved further attention to the UAV-allowed surveillance model facilitating objective detection, and tracking procedure and significantly enhancing the visual surveillance outcomes. Earlier methods to resolve the scene classification method dependent upon feature coding systems with unsupervised feature learning or low-level hand-engineered features can make mid-level image features with limited representational capabilities that usually limit them from the achievement of effectual outcomes. The development of convolutional neural networks (CNNs) helps to attain an efficient classification process in the area of image classification. This paper introduces a Pelican Optimization Algorithm with Convolutional-Recurrent Hop-Field Neural Network (POA-CRHFNN) model for the UAV image classification model. The presented POA-CRHFNN method initially involves preprocessing in two stages namely Gaussian Filter (GF) based noise elimination and contrast enhancement. In addition, the POA-CRHFNN method exploits the ShuffleNetv2 CNN model for feature vector generation. For aerial image classification, the CRHFNN model is used, which allocates different types of classes to the aerial images. The combination of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) in the CRHFNN can capture both spatial and temporal dependencies in aerial images. The integration of the Hopfield Neural Network (HNN) can recognize and classify aerial images based on learned patterns and associations. Finally, the POA is applied for fine-tuning the hyperparameters of the CRHFNN model. By leveraging the behavioural patterns of pelicans, the POA may explore the search space effectively and potentially find better hyperparameter configurations for improved classification performance. The effectiveness of the POA-SCNN model can be investigated on a benchmark aerial image database and the simulation outcomes reported the higher outcome of the POA- CRHFNN method over existing techniques with maximum accuracy of 99.77%, precision of 98.01%, recall of 97.52%, and F-score of 97.69%. [ABSTRACT FROM AUTHOR]

The nonlinear characteristic of activation function is a critical aspect that affects the performance of artificial neural networks (ANNs). Despite its importance, the impact of neuronal nonlinearity variations on the dynamics of ANNs has not been thoroughly studied in previous research. This paper aims to fill this gap by exploring the influence of nonlinearity changes in activation function due to memristive electromagnetic induction on the dynamical characteristics of ANNs. We first propose a memristor model with sinusoidal conductance function. Then, the effects on the biological neuron under the electromagnetic induction are simulated by replacing the gradient of hyperbolic tangent activation function with the conductance of the proposed memristor. Furthermore, a Hopfield neural network (HNN) is constructed by taking the nonlinearity changes of activation function into consideration and its dynamical behaviors are analyzed through Lyapunov exponent spectra, bifurcation diagram, biparameter-based dynamic maps and phase portraits. The numerical simulation results show complex dynamical behaviors such as single-scroll chaotic spiral attractor, double-scroll chaotic attractors and initial-value-dependent offset boosted attractors, demonstrating that nonlinearity changes of activation function induced by the electromagnetic induction have a significant impact on the dynamics of HNN. To further verify our findings, we implement the proposed HNN in hardware and find that the results are in line with our numerical simulations. Finally, we apply the chaotic HNN in the mobile robot path planning task, which achieves higher coverage rate than the random number-based random walk method. [ABSTRACT FROM AUTHOR]

In this paper, based on event-triggered control, the stabilisation problem of time-varying delay switched linear system with all subsystems unstable is studied. Firstly, the idea of event-triggered mechanism is introduced, and the state feedback controller is designed. Combining the discretised linear Lyapunov function method with the average dwell time technique, the stabilisation schemes for continuous switched system with unstable modes are obtained. Secondly, compared with existing results, the event-triggered mechanism scheme adopted under the current event-triggered control strategy reduces the number of system triggers, effectively saves computational resources, avoids Zeno's behaviour, and has better performance in terms of sampling frequency. Finally, the idea of event-triggered mechanism is first extended to discrete time-varying delay switched systems where all subsystems are unstable. By solving linear matrix inequalities, sufficient conditions for global exponential stability of the system are obtained. The effectiveness of this method was verified through a simulation example of a turbofan engine model. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of performanceguaranteed control for discrete-time systems under communication constraints. To alleviate communication burdens, an event-triggered mechanism and quantized data-based protocol is presented. The protocol integrates the advantages of the dualthreshold event-triggered mechanism and signal quantization, leading to a reduced channel occupancy rate compared to the normal weighted try-once-discard protocol and dual-threshold event-triggered protocol. Building upon this protocol, a state feedback controller relying on scheduling signals is proposed. A criterion on stability and energy-to-peak performance is established using the Lyapunov function method and some inequality approaches. Then, a numerically tractable method for determining the desired controller gain via solving linear matrix inequalities. Finally, a double-sided linear switched reluctance machine system is used as an example to illustrate the effectiveness of the designed protocol and the controller. [ABSTRACT FROM AUTHOR]

The discrete Hopfield neural network 3-satisfiability (DHNN-3SAT) model represents an innovative application of deep learning techniques to the Boolean SAT problem. Existing research indicated that the DHNN-3SAT model demonstrated significant advantages in handling 3SAT problem instances of varying scales and complexities. Compared to traditional heuristic algorithms, this model converged to local minima more rapidly and exhibited enhanced exploration capabilities within the global search space. However, the model faced several challenges and limitations. As constraints in SAT problems dynamically increased, decreased, or changed, and as problem scales expanded, the model's computational complexity and storage requirements may increase dramatically, leading to reduced performance in handling large-scale SAT problems. To address these challenges, this paper first introduced a method for designing network synaptic weights based on fundamental logical clauses. This method effectively utilized the synaptic weight information from the original SAT problem within the DHNN network, thereby significantly reducing redundant computations. Concrete examples illustrated the design process of network synaptic weights when constraints were added, removed, or updated, offering new approaches for managing the evolving constraints in SAT problems. Subsequently, the paper presented a DHNN-3SAT model optimized by genetic algorithms combined with K-modes clustering. This model employed genetic algorithm-optimized K-modes clustering to effectively cluster the initial space, significantly reducing the search space. This approach minimized the likelihood of redundant searches and reduced the risk of getting trapped in local minima, thus improving search efficiency. Experimental tests on benchmark datasets showed that the proposed model outperformed traditional DHNN-3SAT models, DHNN-3SAT models combined with genetic algorithms, and DHNN-3SAT models combined with imperialist competitive algorithms across four evaluation metrics. This study not only broadened the application of DHNN in solving 3SAT problems but also provided valuable insights and guidance for future research. [ABSTRACT FROM AUTHOR]

Markovian jump Hopfield NNs (MJHNNs) have received considerable attention due to their potential for application in various areas. This paper deals with the issue of state estimation concerning a category of MJHNNs with discrete and distributed delays. Both time-invariant and time-variant discrete delay cases are taken into account. The objective is to design full-order state estimators such that the filtering error systems exhibit exponential stability in the mean-square sense. Two sufficient conditions on the mean-square exponential stability of MJHNNs are established utilizing augmented Lyapunov-Krasovskii functionals, the Wirtinger-based integral inequality, the Bessel-Legendre inequality, and the convex combination inequality. Then, linear matrix inequalities-based design methods for the required estimators are developed through eliminating nonlinear coupling terms. The feasibility of these linear matrix inequalities can be readily verified via available Matlab software, thus enabling numerically tractable implementation of the proposed design methods. Finally, two numerical examples with simulations are provided to demonstrate the applicability and less conservatism of the proposed stability criteria and estimators. Lastly, two numerical examples are given to demonstrate the applicability and reduced conservatism of the proposed stability criteria and estimator design methods. Future research could explore further refinement of these analysis and design results, and exporing their extention to more complex neural network models. [ABSTRACT FROM AUTHOR]

This paper is dedicated to studying the mean square exponential stability of switched stochastic time‐varying delay neural networks with asynchronous switching aperiodic intermittent control. By utilizing the Halanay‐type inequality and designing appropriate asynchronous switching aperiodic intermittent control, several novel stability criteria of switched stochastic delay neural networks with asynchronous aperiodic intermittent control are presented under the Lyapunov function method and Lyapunov functional method. Among them, asynchronous switching aperiodic intermittent controllers are more practical and flexible compared to state feedback controllers. Finally, we provide two examples to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Resistive memory devices feature drastic conductance change and fast switching dynamics. Particularly, nonvolatile bipolar switching events (set and reset) can be regarded as a unique nonlinear activation function characteristic of a hysteretic loop. Upon simultaneous activation of multiple rows in a crosspoint array, state change of one device may contribute to the conditional switching of others, suggesting an interactive network existing in the circuit. Here, we prove that a passive resistive switching circuit is essentially an attractor network, where the binary memory devices are artificial neurons while the pairwise voltage differences define an anti-symmetric weight matrix. An energy function is successfully constructed for this network, showing that every switching in the circuit would decrease the energy. Due to the nonvolatile hysteretic function, the energy change for bit flip in this network is thresholded, which is different from the classic Hopfield network. It allows more stable states stored in the circuit, thus representing a highly compact and efficient solution for associative memory. Network dynamics (towards stable states) and their modulations by external voltages have been demonstrated in experiment by 3-neuron and 4-neuron circuits. The switching dynamics in resistive memory hardware enables efficient computations, such as stateful logic and temporal information processing. The authors show that a passive resistive switching circuit represented as an attractor network model provides high-capacity, compact and efficient solution for associative memory. [ABSTRACT FROM AUTHOR]

The growing utilization of neural networks has led to a heightened focus on the hardware implementation of such networks. Security concerns associated with these implementations pose a significant challenge in this regard. Among these problems, the vulnerability of these networks against side-channel attacks such as power attacks can be mentioned. This paper presents a technique to enhance the resilience of hardware implementations of neural networks, particularly Hopfield neural networks, to mitigate the risks posed by power attacks. In addition to the fact that the proposed method makes it impossible to attack the network, it also reduces the power consumption of the entire circuit by reducing the leakage currents. The simulation results demonstrate that the proposed approach also achieves about a 10% reduction in energy consumption while concurrently improving the accuracy of the implemented associative memory by 1.1%. [ABSTRACT FROM AUTHOR]

In the present study, we analyze dynamics and bifurcations of a discrete-time Hopfield neural network based on two neurons and the same time delay. We determine stability and bifurcations of the system consisting flip, pitchfork and Neimark-Sacker bifurcations. The normal form coefficients for the all bifurcations are calculated using reducing to the corresponding center manifold, then these coefficients are numerically obtained using MatContM. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors. [ABSTRACT FROM AUTHOR]

Stability is one of the major challenges in organic semiconductor based optoelectronic devices. A comparative study of thermally activated delayed fluorescence (TADF) based organic light emitting diodes (OLEDs) with alkali-halide lithium fluoride (LiF) vs alkaline halide magnesium fluoride (MgF2) inorganic electron injection interlayers is presented. A TADF emitter 4CzIPN doped in CBP is used as an active layer (thickness = 15 nm @6wt. % doping) in an OLED structure: Glass/ITO/PEDOT:PSS/NPD/CBP/CBP:4CzIPN/TPBi/interlayer/Al. Prior to this comparative study, a separate exercise is carried out to obtain an optimal thickness of an MgF2 interlayer on the basis of leakage current and efficiency in the TADF-OLEDs. OLEDs with an LiF interlayer showed an external quantum efficiency (EQE) of 19.7% in comparison with an MgF2 interlayer-based OLED showed slightly lower average EQE ∼19.1% at a luminance level of 100 cd/m2; these efficiency numbers are averaged over ∼60 OLEDs. These slight changes in EQE are supported by the relative photoluminescence quantum yield measurements with a whole device stack. However, alkaline halide MgF2 based TADF-OLEDs showed approximately seven-fold enhancement in the stability (LT60) under identical operating conditions. In situ photoluminescence monitoring of operational TADF-OLEDs confirmed that the probable cause of reduced lifetime is degradation of an LiF/TPBi interface. [ABSTRACT FROM AUTHOR]

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This note is to make some corrections on the assumptions in Theorems 1.2, 1.3, and 1.5 in our paper [Halil Ibrahim Kurt and Wenxian Shen, Journal of Differential Equations 355 (2023) 248–295]. [ABSTRACT FROM AUTHOR]

This paper investigates the coupled Patlak–Keller–Segel–Navier–Stokes (PKS–NS) system in two-dimensional bounded domains with a focus on global well-posedness and the formation of striking patterns, in which the boundary conditions are Neumann conditions for the cell density and the chemical concentration, and the Navier slip boundary condition with zero friction for the fluid velocity. We prove that the solution of the system exists globally in time in the case of subcritical mass. Concerning the critical mass case, we construct the boundary spot steady states rigorously via the inner-outer gluing method. While studying the global existence and the concentration phenomenon of the chemotaxis–fluid model, we develop the global W 2 , p theory for the 2D stationary Stokes system subject to Navier boundary conditions with zero friction and further establish semigroup estimates of the nonstationary counterpart by analyzing the Stokes eigenvalue problem. [ABSTRACT FROM AUTHOR]

We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We then apply our results to quantum generalized Hopfield associative memories. Here we show that, asymptotically and at the description level of quantum fluctuations, only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations. [ABSTRACT FROM AUTHOR]

This paper examines a three-dimensional delayed discrete neural network model analytically and numerically to determine the existence of different types of bifurcations of the involved fixed points. The model exhibits different bifurcations such as pitchforks, flips, Neimark–Sackers, and flip-Neimark–Sackers. The critical coefficients are used to determine the structure of each bifurcation. The curves are calculated and plotted for each bifurcation when the parameters are changed. Further, these bifurcations are theoretically analyzed and numerically verified. From the obtained results, we observed that by drawing the curves associated with each bifurcation, the numerical simulations are consistent with the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, the state observer for coupled cyclic genetic regulatory networks with time delays is designed. The coupling network is composed of two cyclic genetic subnets, which inhibit each other directly. By constructing a suitable Lyapunov – Krasovskii functional velated to the eyclic struction, the delay-dependent stability criteria of the error system are investigated in the form of linear matrix inequalities. Thereby, the state observer of the considered genetic regulatory networks is obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

During the planning stages of new factories for the Body-In-White assembly, the processes used per production system need to be defined. Each production system uses a specific combination of processes, with each process belonging to a main process group. The combination of the processes and groups is subject to restrictions. Since the amount of possible combinations is too large to individually check for restrictions, we propose a Neural Network using an energy measurement derived from Hopfield networks. The proposed network memorizes former correct combinations and provides a recommendation score on how likely a new planned configuration is. Since processes can be paired with processes from their own group or with themselves, the Neural Network is modified to allow loops for joining vertices with themselves. This modification is achieved by adjusting the energy function of Hopfield networks to measure the activation of the combinations of clusters, meaning the edges, and not the activation of vertices during the training phase. We implemented the network for the process planning of factories of a leading European automotive manufacturer, and the results using correct, incorrect, and random process combinations indicate a strong capability of detecting anomalous process combinations. [ABSTRACT FROM AUTHOR]

Evaluating behavioral patterns through logic mining within a given dataset has become a primary focus in current research. Unfortunately, there are several weaknesses in the research regarding the logic mining models, including an uncertainty of the attribute selected in the model, random distribution of negative literals in a logical structure, non-optimal computation of the best logic, and the generation of overfitting solutions. Motivated by these limitations, a novel logic mining model incorporating the mechanism to control the negative literal in the systematic Satisfiability, namely Weighted Systematic 2 Satisfiability in Discrete Hopfield Neural Network, is proposed as a logical structure to represent the behavior of the dataset. For the proposed logic mining models, we used ratio of r to control the distribution of the negative literals in the logical structures to prevent overfitting solutions and optimize synaptic weight values. A new computational approach of the best logic by considering both true and false classification values of the learning system was applied in this work to preserve the significant behavior of the dataset. Additionally, unsupervised learning techniques such as Topological Data Analysis were proposed to ensure the reliability of the selected attributes in the model. The comparative experiments of the logic mining models by utilizing 20 repository real-life datasets were conducted from repositories to assess their efficiency. Following the results, the proposed logic mining model dominated in all the metrics for the average rank. The average ranks for each metric were Accuracy (7.95), Sensitivity (7.55), Specificity (7.93), Negative Predictive Value (7.50), and Mathews Correlation Coefficient (7.85). Numerical results and in-depth analysis demonstrated that the proposed logic mining model consistently produced optimal induced logic that best represented the real-life dataset for all the performance metrics used in this study. [ABSTRACT FROM AUTHOR]

This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some suffcient conditions for ensuring pth moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coeffscients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the existence, uniqueness and stability of solutions for some nonlocal impulsive evolution problems involving conformable fractional derivative. The main results are based on fixed point theorems combined with the semigroup theory. As applications, we give an example to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Different from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality Eα(t)≤1αexp(t1α)(0<α<1)$$ {E}_{\alpha }(t)\le \frac{1}{\alpha}\exp \left({t}^{\frac{1}{\alpha }}\right)\kern0.3em \left(0<\alpha <1\right) $$, by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with α=1$$ \alpha =1 $$ are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This article is concerned with the issue of observer‐based event‐triggered H∞$$ {H}_{\infty } $$ control for networked switched systems (NSSs) under hybrid attacks. Since hybrid attacks can cause more damage to the system than a single cyber attack, this article considers a situation where stochastic deception attacks and aperiodic denial‐of‐service (DoS) attacks coexist in NSSs. To address this issue, the dynamics of the initial switched system combined with the event‐triggered mechanism (ETM), observers and hybrid attacks are formulated as a new augmented switched system. Thereinto, the unmeasurable states are estimated by a newly constructed gain adjustable observer and an observer state‐based adaptive ETM is designed under DoS attacks to save limited communication resources. Then, employing the Lyapunov stability theory and average dwell time (ADT) approach, sufficient conditions are obtained to guarantee the mean‐square exponential stability with a H∞$$ {H}_{\infty } $$ performance index of the new model. And the quantitative relationship between the switching signal and DoS attacks is formulated. Moreover, a co‐design method of ETM parameters and observer‐based controller gains is proposed. Compared with some existent results, restrictions on DoS attack signals and switching signals are relaxed. Finally, a numerical example is utilized to verify the feasibility and effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

This paper investigates the global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays. First, the model of fractional-order inertial memristive neural network with time-varying delays is proposed, which is more universal and less conservative than the integer-order inertial memristive neural network with time-varying delays. Second, one lemma about the compound property of Caputo fractional derivative and integral is given. According to the compound property of Caputo fractional derivative and appropriate variable substitution, the original inertial memristive system translates a routine inertial memristive system. And, using the Filippov discontinuous theory, Lyapunov stability theory, and Mittag-Leffler convergence, several sufficient conditions are derived to ensure the global Mittag-Leffler synchronization of Caputo fractional-order inertial memristive neural networks. An effective feedback controller is proposed for fractional-order inertial memristive neural networks with time-varying delays, such that the global Mittag-Leffler synchronization between the slave system and the master system can be achieved. Finally, a simulation example is given to verify the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the input-to-state stability (ISS) and uniform stability for impulsive nonlinear systems with delayed impulses, where delays are flexible between two consecutive impulsive instants. Illustrating effects caused by delays, concepts of generalised average impulsive delay and generalised reverse average impulsive delay are introduced, and more applicable in practice. Moreover, sufficient conditions for stability properties are formulated with destabilising and stabilising impulses through a general candidate ISS-Lyapunov function and the generalised conditions. It is shown that the double effects of delays in impulses (i.e. stabilising an initial unstable system, or contrarily, destabilising an initial stable system) coincide with the existing results using the exponential candidate ISS-Lyapunov function. Finally, two examples are provided to demonstrate our developed techniques. [ABSTRACT FROM AUTHOR]

The coupling between neurons can lead to diverse neural network architectures, with the Hopfield neural network (HNN) being particularly noteworthy for its resemblance to human brain function and its potential in modeling chaotic systems. This paper introduces a novel approach: a fractional-order HNN coupled with a hyperbolic tangent-type memristor. Initially, we propose a new model for the hyperbolic tangent-type memristor and fingerprints. Subsequently, we construct a memristor-coupled fractional-order Hopfield neural network (mFOHNN) and explore its dynamic behavior using various analytical tools, including phase diagrams, bifurcation diagrams, Lyapunov exponent diagrams, Poincaré maps, and attractor basins. Our findings reveal rich coexisting bifurcation behavior in the neural network model, influenced by different initial values of coexisting attractors. Finally, we validate the model through analysis and implementation using Multisim circuit simulation software and FPGA hardware, respectively. [ABSTRACT FROM AUTHOR]

To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function include multiple time delays, but the memristive connection weights also consider transmission delays. Stemming from the characteristics of neural networks, two different types of discontinuous controllers with state information and sign functions are devised to effectuate network synchronization objectives. Combining the finite-time convergence criterion and the theory of fractional-order calculus, Mittag-Leffler synchronization conditions for fractional-order multi-delayed memristive neural networks (FMMNNs) are derived, and the upper bound of the setting time can be confirmed. Unlike previous jobs, this article focuses on applying different inequality techniques in the synchronous analysis process, rather than comparison principles to manage the multi-delay effects. In addition, this study removes the restrictive requirement that the activation function has a zero value at the switching jumps, and the discontinuous control protocol in this paper makes the networks achieve synchronization over a finite time, with some advantages in terms of the convergence speed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study a free boundary problem on the evolution of a radial tumor with triple-layered structure. Based on the nutrient thresholds $ \sigma_Q $ and $ \sigma_D $, cells in the tumor spheroid are divided into three types, i.e. proliferating cells, quiescent cells and necrotic cells, hence it forms a layered structure from tumor's surface to its center. The novelty of this paper is that the growth of the triple-layered tumor is first taken into rigorous analysis, and the difficulty arises from the two unknown moving interfaces $ \eta $ and $ \rho $ between different cell layers inside the tumor. We show existence and uniqueness of the stationary solution to the system for different external nutrient supply $ \bar \sigma $. It is proved that there exist two constants $ \sigma^* $ and $ \sigma_* $ with the relation $ \sigma^*> \sigma_*>\tilde \sigma $, such that if $ \bar \sigma> \sigma^* $, the dormant tumor forms a triple-layered structure; if $ \sigma_*<\bar \sigma \le \sigma^* $, the dormant tumor has double layers with proliferating cells and quiescent cells; if $ \tilde \sigma <\bar \sigma\le \sigma_* $, the dormant tumor is filled with only proliferating cells and appears as a single layer; and if $ \bar \sigma\le\tilde \sigma $, the dormant tumor vanishes. The asymptotic stability of the stationary solution above is also studied. We can show the tendency of the evolutionary tumor towards its dormant state by using only $ \bar \sigma $ and the initial radius $ R_0 $ as well. [ABSTRACT FROM AUTHOR]

This study develops a "Skill Talent Ecological Evaluation Model" across cultivation, potential energy, kinetic energy, innovation, and service and support ecologies. AHP-entropy determines indicator weights, Hopfield neural network assesses talent ecology levels, and the PVAR model analyzes digital transformation effects. Findings reveal: Cultivation ecology rates A, potential ecology rates B+, kinetic ecology rates B-, service and support ecology rates B-, and innovation ecology rates C. Digital transformation spurs skill demand, impacting talent and economic contributions. Kinetic ecology sees increased demand, potentially impacting traditional industries positively. Innovation ecology necessitates continuous skill learning. Service and support ecology witnesses growth in digital entrepreneurship, requiring policy incentives and incubation center support. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for a solid spherically symmetric vascular tumor growth with nutrient periodic supply and time delays is studied. Compared to the apoptosis process of tumor cells, there is a time delay in the process of tumor cell division. The cells inside the tumor obtain nutrient σ(r,t) through blood vessels, and the tumor attracts blood vessels at a rate proportional to α(t). So, the boundary value condition ∂σ ∂r + α(t)(σ − ψ(t)) = 0,r = R(t),t > 0, holds on the boundary, where the function ψ(t) is the concentration of nutrient externally supplied to the tumor. Considering that the nutrients provided by the outside world are often periodic, the research in this paper assumes that ψ(t) is a periodic function. Sufficient conditions for the global stability of zero steady state are presented. Under certain conditions, we prove that there exists at least one periodic solution to the model. The results are illustrated by computer simulations. [ABSTRACT FROM AUTHOR]

In modern power systems, the uncertainty and volatility of generation and loads greatly increase the balance discrepancy between the power supply and demand, creating major potential security hazards. To limit out‐of‐bound frequencies, an effective frequency control method for power systems with interval uncertain disturbances is proposed. Based on the state space model of the system frequency response with delays, linear matrix inequalities are constructed based on the input‒output finite‐time stability of the system frequency. By searching for the output feedback gain and altering the time delay with the Padé approximation, the feasibility of the linear matrix inequalities is improved, and a frequency controller is designed. The simulation results show that the proposed method can effectively control frequency deviations. When the closed‐loop system is disturbed by uncertain power fluctuations, its frequency will always remain within the allowable range to ensure the secure operation of the power system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

There exist numerous multi‐path signals with impulsive noise (IN) in a multi‐path propagation environment. The direction‐of‐arrival (DOA) is highly challenging to be assessed because of the strong IN. For various military along with civilian applications, DOA estimation has turned into a hopeful technology. But, estimating DOA for multipath signals with IN environments is extremely complicated. A desirable output is not attained by several existent techniques, namely subspace‐centric approaches, maximum likelihood techniques, along with sparse representation‐centric methods, for DOA assessment. Therefore, an effective satin bowerbird optimization‐based deep learning neural network centered DOA estimation upon single snapshots is proposed in this paper for attaining robust and precise DOA estimation in multipath and IN environments. An arbitrary array configuration is employed by utilizing the proposed work as an input signal for establishing the received signal's model. Pre‐processing, time‐frequency domain conversion, feature extraction, feature reduction and DOA estimation are the proposed method's 5 disparate stages. To evince the proposed model's efficacy, its outcomes are analogized with other prevailing techniques regarding some performance metrics. The proposed model attains the root mean square error of 0.6484366‐AZ and 0.6484366‐EA, root mean squared percentage error (RMPSE) of 4.636107‐AZ and 5.628599‐EA and probability of resolution of 0.967999‐AZ and 0.962841‐EA, which are extremely less when compared to the prevailing methods; thus, depicting the superiority of the proposed model for an effective DOA estimation. [ABSTRACT FROM AUTHOR]

This paper investigates the impulsive stability analysis issues of discrete-time positive singular systems with time delay. First, the paper addresses the positivity problem of the system by providing sufficient conditions. Next, a new method based on state transformations is presented to derive a new delay-dependent criterion for the exponential stability of impulsive positive singular systems. Finally, the effectiveness of the proposed conditions is validated through three numerical examples. [ABSTRACT FROM AUTHOR]

The concept of perfect equilibrium, formulated by Selten (Int J Game Theory 4:25–55, 1975), serves as an effective characterization of rationality in strategy perturbation. In our study, we propose a modified version of perfect equilibrium that incorporates perturbation control parameters. To match the beliefs with the equilibrium choice probabilities, the logistic quantal response equilibrium (logistic QRE) was established by McKelvey and Palfrey (Games Econ Behav 10:6–38, 1995), which is only able to select a Nash equilibrium. By introducing a linear combination between a mixed strategy profile and a given vector with positive elements, this paper develops a variant of the logistic QRE for the selection of the special version of perfect equilibrium. Expanding upon this variant, we construct an equilibrium system that incorporates an exponential function of an extra variable. Through rigorous error-bound analysis, we demonstrate that the solution set of this equilibrium system leads to a perfect equilibrium as the extra variable approaches zero. Consequently, we establish the existence of a smooth path to a perfect equilibrium and employ an exponential transformation of variables to ensure numerical stability. To make a numerical comparison, we capitalize on a variant of the square-root QRE, which yields another smooth path to a perfect equilibrium. Numerical results further verify the effectiveness and efficiency of the proposed differentiable path-following methods. [ABSTRACT FROM AUTHOR]

One of the significant causes of death globally is cancer (http://www.who.org/). Another critical problem is obesity, which is associated with an increased cancer threat. This work provides insight into how obesity contributes to cancer progression and metastasis. We developed a diffusive obesity-cancer model consisting of cancer cells, normal cells, fat cells, macrophages, and an extracellular matrix (ECM) for this aim. We have directed the formed model's global existence and non-negativity. Equilibrium points for the related ODE are calculated, and its existence and stability study is also done. We present a traveling wave analysis of the obesity-cancer model and have calculated the minimum wave speed. Using a combination of analytic and numerical results of traveling waves, we conjecture that the minimal wave speed depends on fat cells' diffusive rate and haptotaxis coefficient. We followed the theory of the Partial Rank Correlation Coefficient (PRCC) to carry out a global sensitivity analysis to evaluate the most sensitive parameters reliable for cancer progression. We delivered a comprehensive numerical analysis of our deterministic and diffusive models (in 1D and 2D) and analogized the result. Numerical simulation of corresponding spatially explicit systems conveys complex spatio-temporal dynamics, resulting in the appearance of patterns. It also discloses that cancer spread increases with increased haptotaxis coefficient and growth rate of obese cells. Our simulation confirms that the degradation of the ECM increases cancer spread and density. [ABSTRACT FROM AUTHOR]

A stochastic budworm growth model with periodic coefficients is formulated and explored. Sufficient conditions for the existence of a unique ergodic periodic measure are given. An example based on exemplary data is also provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

Excitable systems have important biological applications, such as impulse transmission in neurons. The Chialvo map and Rulkov map are popular and important for studying the nonlinear dynamics of neurons. Both belong to the family of two-dimensional maps used to describe excitable systems in general and neural dynamics in particular. They show rich dynamics ranging from oscillatory, bursting to chaotic bursting behaviour. Neurons have memory and extension of the above maps to fractional order is an efficient way to model the effects of memory. This generalisation provides a wider scope of understanding the neuron systems. We study the dynamics of the above maps for fractional orders. We observe that whether the chaotic range is suppressed, enhanced or remains unchanged depends on the details of the eigenvalues of Jacobian obtained by the linearisation around the fixed point. We show that the three cases studied give three different results. The impact of fractional order on the efficacy of feedback control as well as the frequency and amplitude of bursts in the chaotic region is different for different maps. Thus, the impact of memory on the stability of neuronal maps depends on the details of the underlying system. [ABSTRACT FROM AUTHOR]

Economic growth is resulting in serious environmental problems. Effectively establishing an economic growth model that considers environmental pollution is an important topic. To analyze the interplay between economic growth and environmental pollution, a fractional-order time-delayed economic growth model with environmental purification is proposed in this paper. The established model considers not only the environment and economic production but also the labor force population and total factor productivity. Furthermore, the asymptotic stability conditions and parameter stability interval are provided. Finally, in numerical experiments, the correctness of the theory is verified. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA for highly nonlinear neutral differential systems. The cases of bounded non-differentiable delays and unbounded proportional delays are discussed, respectively. Subsequently, by utilizing the proposed lemmas, combining the Lyapunov stability theory and inequality technique, the estimation of DOA on HNNCNs with bounded delays or proportional delays is derived when the chosen control gain is sufficiently large. If initial values start from DOA, then the states of systems will exponentially or polynomially converge to the equilibrium point, which means that the local exponential or polynomial synchronization of HNNCNs is realized. Additionally, the weighted outer-coupling matrix of complex networks is not required to be symmetric, which means that the derived results can be applied to both the undirected networks and directed networks. Finally, several numerical examples are provided to illustrate the feasibility of theoretical findings. [ABSTRACT FROM AUTHOR]