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Keywords = impulsive diffusion

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21 pages, 5942 KiB  
Article
White Matter Microstructural Abnormalities in Children with Familial vs. Non-Familial Attention-Deficit/Hyperactivity Disorder (ADHD)
by Rahman Baboli, Kai Wu, Jeffrey M. Halperin and Xiaobo Li
Biomedicines 2025, 13(3), 676; https://doi.org/10.3390/biomedicines13030676 - 10 Mar 2025
Viewed by 956
Abstract
Background: Attention-deficit/hyperactivity disorder (ADHD) is a highly prevalent, heterogeneous neurodevelopmental disorder. Methods: This study presents, for the first time, a comprehensive investigation of white matter microstructural differences between familial ADHD (ADHD-F) and non-familial ADHD (ADHD-NF) using advanced diffusion tensor imaging analyses [...] Read more.
Background: Attention-deficit/hyperactivity disorder (ADHD) is a highly prevalent, heterogeneous neurodevelopmental disorder. Methods: This study presents, for the first time, a comprehensive investigation of white matter microstructural differences between familial ADHD (ADHD-F) and non-familial ADHD (ADHD-NF) using advanced diffusion tensor imaging analyses in a large community-based sample. Results: Children with ADHD-F exhibited significantly greater volume in the right anterior thalamic radiations and the left inferior fronto-occipital fasciculus compared to controls, and greater volume in the left inferior longitudinal fasciculus relative to ADHD-NF. The ADHD-NF group showed reduced fractional anisotropy in the left inferior longitudinal fasciculus compared to the controls. In both the ADHD-F and ADHD-NF groups, a greater volume of anterior thalamic radiation significantly contributed to reduced ADHD symptoms. Conclusions: Our findings suggest that white matter microstructural alterations along the frontal-thalamic pathways may play a critical role in hereditary factors among children with ADHD-F and significantly contribute to elevated inattentive and hyperactive/impulsive behaviors in the affected children. Full article
(This article belongs to the Special Issue Applications of Imaging Technology in Human Diseases)
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13 pages, 3960 KiB  
Article
Vestibular Testing Results in a World-Famous Tightrope Walker
by Alexander A. Tarnutzer, Fausto Romano, Nina Feddermann-Demont, Urs Scheifele, Marco Piccirelli, Giovanni Bertolini, Jürg Kesselring and Dominik Straumann
Clin. Transl. Neurosci. 2025, 9(1), 9; https://doi.org/10.3390/ctn9010009 - 17 Feb 2025
Viewed by 760
Abstract
Purpose: Accurate and precise navigation in space and postural stability rely on the central integration of multisensory input (vestibular, proprioceptive, visual), weighted according to its reliability, to continuously update the internal estimate of the direction of gravity. In this study, we examined both [...] Read more.
Purpose: Accurate and precise navigation in space and postural stability rely on the central integration of multisensory input (vestibular, proprioceptive, visual), weighted according to its reliability, to continuously update the internal estimate of the direction of gravity. In this study, we examined both peripheral and central vestibular functions in a world-renowned 53-year-old male tightrope walker and investigated the extent to which his exceptional performance was reflected in our findings. Methods: Comprehensive assessments were conducted, including semicircular canal function tests (caloric irrigation, rotatory-chair testing, video head impulse testing of all six canals, dynamic visual acuity) and otolith function evaluations (subjective visual vertical, fundus photography, ocular/cervical vestibular-evoked myogenic potentials [oVEMPs/cVEMPs]). Additionally, static and dynamic posturography, as well as video-oculography (smooth-pursuit eye movements, saccades, nystagmus testing), were performed. The participant’s results were compared to established normative values. High-resolution diffusion tensor magnetic resonance imaging (DT-MRI) was utilized to assess motor tract integrity. Results: Semicircular canal testing revealed normal results except for a slightly reduced response to right-sided caloric irrigation (26% asymmetry ratio; cut-off = 25%). Otolith testing, however, showed marked asymmetry in oVEMP amplitudes, confirmed with two devices (37% and 53% weaker on the left side; cut-off = 30%). Bone-conducted cVEMP amplitudes were mildly reduced bilaterally. Posturography, video-oculography, and subjective visual vertical testing were all within normal ranges. Diffusion tensor MRI revealed no structural abnormalities correlating with the observed functional asymmetry. Conclusions: This professional tightrope walker’s exceptional balance skills contrast starkly with significant peripheral vestibular (otolithic) deficits, while MR imaging, including diffusion tensor imaging, remained normal. These findings highlight the critical role of central computational mechanisms in optimizing multisensory input signals and fully compensating for vestibular asymmetries in this unique case. Full article
(This article belongs to the Section Clinical Neurophysiology)
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21 pages, 335 KiB  
Article
On the Global Practical Exponential Stability of h-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays
by Gani Stamov, Trayan Stamov, Ivanka Stamova and Cvetelina Spirova
Entropy 2025, 27(2), 188; https://doi.org/10.3390/e27020188 - 12 Feb 2025
Viewed by 776
Abstract
In this paper, we focus on h-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The [...] Read more.
In this paper, we focus on h-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The states of interest are determined by the so-called h-manifolds, i.e., manifolds defined by a specific function h, which is essential for various applied problems in imposing constraints on their dynamics. The established criteria are less restrictive for the variable domain and diffusion coefficients. The effect of some uncertain parameters on the stability behavior is also considered and a robust practical stability analysis is proposed. In addition, the obtained h-manifolds’ practical stability results are applied to a bidirectional associative memory (BAM) neural network model with impulsive perturbations and time-varying delays. Appropriate examples are discussed. Full article
(This article belongs to the Special Issue Dynamics in Complex Neural Networks, 2nd Edition)
17 pages, 31244 KiB  
Article
Mechanical Properties and High-Temperature Steam Oxidation of Cr/CrN Multi-Layers Produced by High-Power Impulse Magnetron Sputtering
by Ding Chen, Daoxuan Liang, Wei Dai, Qimin Wang, Jun Yan and Junfeng Wang
Coatings 2025, 15(2), 185; https://doi.org/10.3390/coatings15020185 - 6 Feb 2025
Viewed by 987
Abstract
In this study, Cr coatings, CrN coatings, and CrN/Cr multi-layer coatings were deposited on the surface of Zr-4 alloy by high-power impulse magnetron sputtering (HiPIMS). We have investigated the effect of coating structure on the microstructure, mechanical properties, and high-temperature steam oxidation properties [...] Read more.
In this study, Cr coatings, CrN coatings, and CrN/Cr multi-layer coatings were deposited on the surface of Zr-4 alloy by high-power impulse magnetron sputtering (HiPIMS). We have investigated the effect of coating structure on the microstructure, mechanical properties, and high-temperature steam oxidation properties of coatings. The results show that the single-layer CrN coating has higher hardness but performs poorly in high-temperature steam oxidation compared to the Cr coating due to its greater brittleness, which makes it prone to cracking and spalling in high-temperature steam environments and provides a channel for Zr diffusion. In multi-layer coatings, however, they form a fine columnar crystal structure and a smoother surface, and the more layers there are, the better the mechanical properties and resistance to high-temperature steam oxidation of the coating. In a high-temperature steam environment, the CrN layer decomposes to form Cr2N and N2, and the N atoms diffuse inwards and react with Zr to form an α-Zr(N) layer, which restricts interdiffusion between Cr and Zr and blocks the diffusion of O into the substrate. Therefore, (CrN/Cr)n coatings with a multi-layer structure have excellent high-temperature steam corrosion resistance. Full article
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19 pages, 894 KiB  
Article
Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks
by Rouzimaimaiti Mahemuti, Abdujelil Abdurahman and Ahmadjan Muhammadhaji
Fractal Fract. 2025, 9(2), 88; https://doi.org/10.3390/fractalfract9020088 - 28 Jan 2025
Cited by 3 | Viewed by 700
Abstract
This study delves into the synchronization issues of the impulsive fractional-order, mainly the Caputo derivative of the order between 0 and 1, bidirectional associative memory (BAM) neural networks incorporating the diffusion term at a fixed time (FXT) and a predefined time (PDT). Initially, [...] Read more.
This study delves into the synchronization issues of the impulsive fractional-order, mainly the Caputo derivative of the order between 0 and 1, bidirectional associative memory (BAM) neural networks incorporating the diffusion term at a fixed time (FXT) and a predefined time (PDT). Initially, this study presents certain characteristics of fractional-order calculus and several lemmas pertaining to the stability of general impulsive nonlinear systems, specifically focusing on FXT and PDT stability. Subsequently, we utilize a novel controller and Lyapunov functions to establish new sufficient criteria for achieving FXT and PDT synchronizations. Finally, a numerical simulation is presented to ascertain the theoretical dependency. Full article
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21 pages, 11129 KiB  
Article
Investigation on Flow Features and Combustion Characteristics in a Boron-Based Solid-Ducted Rocket Engine
by Xiang Tang, Xiaotao Tian, Liang Zhu, Suli Wu, Meng Huang and Weixuan Li
Energies 2025, 18(3), 524; https://doi.org/10.3390/en18030524 - 23 Jan 2025
Viewed by 849
Abstract
Numerical and experimental approaches are conducted to investigate the flow features and secondary combustion performance induced by different air–fuel ratios in a boron-based solid-ducted rocket engine. The results indicated that the afterburning chamber flow features become more complicated owing to the multiple nozzles [...] Read more.
Numerical and experimental approaches are conducted to investigate the flow features and secondary combustion performance induced by different air–fuel ratios in a boron-based solid-ducted rocket engine. The results indicated that the afterburning chamber flow features become more complicated owing to the multiple nozzles of the gas injector, and a number of recirculation zones are generated. Because of this, the mixing of the fuel gas and incoming air is enhanced. When the air–fuel ratio decreases, the heat release in the afterburning chamber increases continuously, which causes the pre-combustion shock train to continue to propagate upstream in the subsonic diffuser of the inlet isolator, along with the boundary layer separation zone also moving forward, and the stability margin of the direct-connect inlet decreasing gradually. Furthermore, the direct-connect inlet works at a critical state with an air–fuel ratio of 11.5. As the mass flow rate of the fuel-rich gas rises gradually, the engine thrust gradually increases, and the number of vortexes in the afterburning chamber and the corresponding region affected by the vortexes generally decrease. Meanwhile, the mixing and combustion of the fuel-rich gas and incoming flow were not substantially changed. Additionally, the combustion efficiency and specific impulse are proportional to the air fuel ratio. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
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22 pages, 331 KiB  
Article
On an Impulsive Conformable M1 Oncolytic Virotherapy Neural Network Model: Stability of Sets Analysis
by Gani Stamov, Ivanka Stamova and Cvetelina Spirova
Mathematics 2025, 13(1), 141; https://doi.org/10.3390/math13010141 - 2 Jan 2025
Viewed by 675
Abstract
In this paper, the impulsive conformable calculus approach is applied to the introduction of an M1 oncolytic virotherapy neural network model. The proposed model extends some existing mathematical models that describe the dynamics of the concentrations of normal cells, tumor cells, nutrients, [...] Read more.
In this paper, the impulsive conformable calculus approach is applied to the introduction of an M1 oncolytic virotherapy neural network model. The proposed model extends some existing mathematical models that describe the dynamics of the concentrations of normal cells, tumor cells, nutrients, M1 viruses and cytotoxic T lymphocyte (CTL) cells to the impulsive conformable setting. The conformable concept allows for flexibility in the modeling approach, as well as avoiding the complexity of using classical fractional derivatives. The impulsive generalization supports the application of a suitable impulsive control therapy. Reaction–diffusion terms are also considered. We analyze the stable behavior of sets of states, which extend the investigations of the dynamics of separate equilibrium points. By applying the impulsive conformable Lyapunov function technique, sufficient conditions for the uniform global exponential stability of sets of states are established. An example is also presented to illustrate our results. Full article
(This article belongs to the Special Issue Algorithms and Models for Bioinformatics and Biomedical Applications)
20 pages, 5525 KiB  
Article
Rarefied Nozzle Flow Computation Using the Viscosity-Based Direct Simulation Monte Carlo Method
by Deepa Raj Mopuru, Nishanth Dongari and Srihari Payyavula
Fluids 2025, 10(1), 2; https://doi.org/10.3390/fluids10010002 - 24 Dec 2024
Viewed by 921
Abstract
Micro-nozzles are essential for enabling precise satellite attitude control and orbital maneuvers. Accurate prediction of performance parameters, including thrust and specific impulse, is critical, necessitating careful design of these nozzles. Given the high Knudsen numbers associated with micro-nozzle flows, rarefied gas dynamics often [...] Read more.
Micro-nozzles are essential for enabling precise satellite attitude control and orbital maneuvers. Accurate prediction of performance parameters, including thrust and specific impulse, is critical, necessitating careful design of these nozzles. Given the high Knudsen numbers associated with micro-nozzle flows, rarefied gas dynamics often dominate, and conventional computational fluid dynamics (CFD) methods fail to capture accurate flow expansion behavior. The Direct Simulation Monte Carlo (DSMC) method, developed by Bird, is widely used for modeling rarefied flows; however, it has been primarily implemented on platforms like OpenFOAM and FORTRAN, with limited exploration in MATLAB. This study presents the development of a viscosity-based DSMC (μDSMC) simulation framework in MATLAB for analyzing rarefied gas expansion through micro-nozzles. Key boundary conditions, including upstream and downstream pressure conditions and thermal wall treatments with diffuse reflection, are incorporated into the code. The μDSMC results are validated against traditional DSMC outcomes, showing strong agreement. Grid convergence studies indicate that the radial grid size must be less than one-third of the mean free path, with a more relaxed requirement on axial grid size. Flow characteristics within micro-nozzles are evaluated across varying ambient pressures and gas species in terms of the back pressure ratio, effective exit flow ratio, and exit flow velocity. Studies indicated that a minimum back pressure ratio is required, beyond which the effective nozzle flow expansion is achieved. Parametric analysis further suggests that gases with lower molecular weights are preferable for achieving optimal expansion in micro-nozzles under low ambient pressures. Full article
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17 pages, 1370 KiB  
Article
Finite-Time Stability Analysis of a Discrete-Time Generalized Reaction–Diffusion System
by Othman Abdullah Almatroud and Adel Ouannas
Mathematics 2024, 12(23), 3679; https://doi.org/10.3390/math12233679 - 24 Nov 2024
Cited by 4 | Viewed by 1158
Abstract
This paper delves into a comprehensive analysis of a generalized impulsive discrete reaction–diffusion system under periodic boundary conditions. It investigates the behavior of reactant concentrations through a model governed by partial differential equations (PDEs) incorporating both diffusion mechanisms and nonlinear interactions. By employing [...] Read more.
This paper delves into a comprehensive analysis of a generalized impulsive discrete reaction–diffusion system under periodic boundary conditions. It investigates the behavior of reactant concentrations through a model governed by partial differential equations (PDEs) incorporating both diffusion mechanisms and nonlinear interactions. By employing finite difference methods for discretization, this study retains the core dynamics of the continuous model, extending into a discrete framework with impulse moments and time delays. This approach facilitates the exploration of finite-time stability (FTS) and dynamic convergence of the error system, offering robust insights into the conditions necessary for achieving equilibrium states. Numerical simulations are presented, focusing on the Lengyel–Epstein (LE) and Degn–Harrison (DH) models, which, respectively, represent the chlorite–iodide–malonic acid (CIMA) reaction and bacterial respiration in Klebsiella. Stability analysis is conducted using Matlab’s LMI toolbox, confirming FTS at equilibrium under specific conditions. The simulations showcase the capacity of the discrete model to emulate continuous dynamics, providing a validated computational approach to studying reaction-diffusion systems in chemical and biological contexts. This research underscores the utility of impulsive discrete reaction-diffusion models for capturing complex diffusion–reaction interactions and advancing applications in reaction kinetics and biological systems. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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31 pages, 1298 KiB  
Systematic Review
Impulsivity in ADHD and Borderline Personality Disorder: A Systematic Review of Gray and White Matter Variations
by Łukasz Franczak, Piotr Podwalski, Patryk Wysocki, Bartosz Dawidowski, Adam Jędrzejewski, Marcin Jabłoński and Jerzy Samochowiec
J. Clin. Med. 2024, 13(22), 6906; https://doi.org/10.3390/jcm13226906 - 16 Nov 2024
Cited by 2 | Viewed by 5126
Abstract
Introduction: Impulsivity is one of the overlapping symptoms common to borderline personality disorder (BPD) and attention deficit hyperactivity disorder (ADHD), but the neurobiological basis of these disorders remains uncertain. This systematic review aims to identify abnormalities in the gray and white matter [...] Read more.
Introduction: Impulsivity is one of the overlapping symptoms common to borderline personality disorder (BPD) and attention deficit hyperactivity disorder (ADHD), but the neurobiological basis of these disorders remains uncertain. This systematic review aims to identify abnormalities in the gray and white matter associated with impulsivity in BPD and ADHD. Methods: We conducted a systematic search of the PubMed, Embase, and SCOPUS databases, adhering to PRISMA guidelines. Studies that investigated gray and white matter alterations in BPD or ADHD populations and their relationship with impulsivity were included. We reviewed information from 23 studies involving 992 participants, which included findings from structural MRI and DTI. Results: The review identified various nonhomogeneous changes associated with impulsivity in BPD and ADHD. BPD was mainly associated with abnormalities in the prefrontal cortex (PFC) and limbic areas, which correlated negatively with impulsivity. In contrast, impulsivity associated with ADHD was associated with structural changes in the caudate nucleus and frontal–striatal pathways. Despite the overlapping symptoms of impulsivity, the neurobiological mechanisms appeared to differ between the two disorders. Conclusions: These findings emphasize the distinct neurostructural correlates of impulsivity in BPD and ADHD. While both disorders show impulsivity as one of their main symptoms, the fundamental brain structures associated with this trait are different. BPD is primarily associated with abnormalities in the prefrontal cortex and limbic system, whereas the alterations seen in ADHD tend to focus on the caudate nucleus and frontostriatal pathways. Further research is needed to clarify these differences and their implications for treatment. Full article
(This article belongs to the Section Mental Health)
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15 pages, 8632 KiB  
Article
Materials That Do Not Form Any Defects After WEDM
by Katerina Mouralova, Jiří Fries, Libor Benes and Pavel Houska
Processes 2024, 12(11), 2448; https://doi.org/10.3390/pr12112448 - 5 Nov 2024
Viewed by 913
Abstract
Wire Electric Discharge Machining (WEDM) is an unconventional machining technology that uses electrical impulses to generate very high temperatures to cut material. The WEDM process hence causes some unfortunate defects, such as cracks and burnt cavities, which can impact the correct functionality of [...] Read more.
Wire Electric Discharge Machining (WEDM) is an unconventional machining technology that uses electrical impulses to generate very high temperatures to cut material. The WEDM process hence causes some unfortunate defects, such as cracks and burnt cavities, which can impact the correct functionality of the machined pieces and shorten their service life. This study was carried out to understand which materials remain defect-free after WEDM. The examined materials were the Ampcoloy 35 copper alloy, the high-entropy steels FeCoCrMnNi and FeCoCrMnNiC0.2, and the B1914 and Nimonic 263 nickel alloys. The influence of the machining parameters, namely the pulse off time, gap voltage, discharge current, pulse on time, and wire feed, on the cutting speed and the surface topography of the machined piece was investigated. The surface morphology, the state of the subsurface layer in a cross-section, and the number of diffused elements from the wire electrode were analysed. All the analysed materials were found completely suitable for WEDM machining as they do not form any surface or subsurface defects. Full article
(This article belongs to the Section Materials Processes)
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24 pages, 6142 KiB  
Article
A Study on the Evolution Laws of Entrainment Performances Using Different Mixer Structures of Ejectors
by Hongjie Chen, Jing Ge and Zhizhou Xu
Entropy 2024, 26(11), 891; https://doi.org/10.3390/e26110891 - 22 Oct 2024
Cited by 1 | Viewed by 1057
Abstract
Being the core of the ejector refrigeration system, an ejector with a suitable mixer, conical–cylindrical or cylindrical, is key to high-energy-efficiency and low-carbon systems. To promote the scientific selection of mixers for ejectors based on the theoretical models that have been validated by [...] Read more.
Being the core of the ejector refrigeration system, an ejector with a suitable mixer, conical–cylindrical or cylindrical, is key to high-energy-efficiency and low-carbon systems. To promote the scientific selection of mixers for ejectors based on the theoretical models that have been validated by experiments, the evolution laws of the entrainment ratios in the two types of ejectors are studied under various operating conditions. Furthermore, the influence mechanism of the mixer structures on the entrainment ratio of the ejector is elucidated by comparing the distribution characteristics of the entropy generation rate, pressure lift proportion, and entropy generation rate of the per-unit pressure lift in the two types of ejectors. The efficiencies of the conical-cylindrical mixer ejector and cylindrical mixer ejector exist a crossover, which makes the entrainment ratio of the conical–cylindrical mixer ejector smaller under small compression ratios but larger under large compression ratios. By changing the cylindrical mixer into a conical one, on the one hand, more pressure rise will be distributed in the diffuser, which helps to reduce the entropy increase rate in the pressurization process; on the other hand, the wall impulse effect of the conical mixer will lead to an increase in entropy generation rate of per-unit pressure lift, resulting in a growing entropy generation rate of boosting. The dominant roles are not the same with changing compression ratios, which leads to different relationships of entrainment ratio between the cylindrical and conical mixer ejectors. Full article
(This article belongs to the Section Thermodynamics)
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18 pages, 10988 KiB  
Article
Thermal Annealing Effect on Elastoplastic Behaviour of Al/Cu Bimetal during Three-Point Bending
by Robert Uścinowicz
Materials 2024, 17(18), 4637; https://doi.org/10.3390/ma17184637 - 21 Sep 2024
Cited by 1 | Viewed by 981
Abstract
This paper presents the results of experimental studies on the effects of temperature and time of annealing on the elastoplastic properties of bimetallic aluminium–copper sheets. Mechanical tests were carried out on flat samples previously heated to temperatures of 250, 350, 450, and 500 [...] Read more.
This paper presents the results of experimental studies on the effects of temperature and time of annealing on the elastoplastic properties of bimetallic aluminium–copper sheets. Mechanical tests were carried out on flat samples previously heated to temperatures of 250, 350, 450, and 500 °C for 40, 90, and 150 min. At the beginning of the tests, the elastic constants and internal friction energy were determined after thermal exposure using the impulse vibration exposure method. Further tests were carried out on the same samples using the three-point bending test. Based on the tests, the following quantities were determined and analysed: elasticity angles, translocations of the neutral axes of the cross-sections of samples, and changes in the values of bending moments plasticizing the extreme layers of bimetallic Al/Cu samples resulting from thermal interactions. The final part of this paper presents the results of measurements of the thickness of diffusion zones at the interface and their effect on the stability of the joint after annealing. The studies that were conducted indicate the dominant influence of the thermal factor on the properties of the Al/Cu bimetal above the temperature of 350 °C, which leads to the weakening of its strength and the degradation of the structure at the metallic phase boundary. Full article
(This article belongs to the Section Advanced Composites)
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15 pages, 439 KiB  
Article
Global Exponential Stability of Impulsive Delayed Neural Networks with Parameter Uncertainties and Reaction–Diffusion Terms
by Fei Luo, Weiyi Hu, Enli Wu and Xiufang Yuan
Mathematics 2024, 12(15), 2395; https://doi.org/10.3390/math12152395 - 31 Jul 2024
Viewed by 973
Abstract
In this paper, we present a method to achieve exponential stability in a class of impulsive delayed neural networks containing parameter uncertainties, time-varying delays, and impulsive effect and reaction–diffusion terms. By using an integro-differential inequality with impulsive initial conditions and employing the M-matrix [...] Read more.
In this paper, we present a method to achieve exponential stability in a class of impulsive delayed neural networks containing parameter uncertainties, time-varying delays, and impulsive effect and reaction–diffusion terms. By using an integro-differential inequality with impulsive initial conditions and employing the M-matrix theory and the nonlinear measure approach, some new sufficient conditions ensuring the global exponential stability and global robust exponential stability of the considered system are derived. In particular, the results obtained are presented by simple algebraic inequalities, which are certainly more concise than the previous methods. By comparisons and examples, it is shown that the results obtained are effective and useful. Full article
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19 pages, 8020 KiB  
Article
Stochastic Synchronization of Impulsive Reaction–Diffusion BAM Neural Networks at a Fixed and Predetermined Time
by Rouzimaimaiti Mahemuti, Ehmet Kasim and Hayrengul Sadik
Mathematics 2024, 12(8), 1204; https://doi.org/10.3390/math12081204 - 17 Apr 2024
Viewed by 1072
Abstract
This paper discusses the synchronization problem of impulsive stochastic bidirectional associative memory neural networks with a diffusion term, specifically focusing on the fixed-time (FXT) and predefined-time (PDT) synchronization. First, a number of more relaxed lemmas are introduced for the FXT and PDT stability [...] Read more.
This paper discusses the synchronization problem of impulsive stochastic bidirectional associative memory neural networks with a diffusion term, specifically focusing on the fixed-time (FXT) and predefined-time (PDT) synchronization. First, a number of more relaxed lemmas are introduced for the FXT and PDT stability of general types of impulsive nonlinear systems. A controller that does not require a sign function is then proposed to ensure that the synchronization error converges to zero within a predetermined time. The controllerdesigned in this paper serves the additional purpose of preventing the use of an unreliable inequality in the course of proving the main results. Next, to guarantee FXT and PDT synchronization of the drive–response systems, this paper employs the Lyapunov function method and derives sufficient conditions. Finally, a numerical simulation is presented to validate the theoretical results. Full article
(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations)
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