Search Results (23)

A distributed weighted fusion fractional order filter is proposed for multi-sensor multi-delay fractional order systems. Firstly, the time-delay system is transformed into a non-time-delay system using the state augmentation method, and the optimal augmented fractional Kalman filter is derived. Secondly, in order to reduce the computational burden, a suboptimal fractional order Kalman filter is presented. Compared with the optimal augmented method, it greatly reduces the computational complexity, which is convenient for real-time applications. Then, in order to derive the weighting coefficient for distributed fusion, the calculation formula of filtering error variance matrix between any two sensor subsystems is derived. Finally, the distributed weighted fusion fractional order filter is presented. It is local optimal and globally suboptimal: compared with each local filter, it has higher accuracy; compared with the centralized fusion filter, it has lower accuracy and more fault tolerance. In summary, it is more suitable for practical application. Simulation results verify the effectiveness of the proposed algorithm. Full article

A new class of linear non-homogeneous discrete matrix equations with multiple delays and second-order differences is considered, where the coefficient matrices satisfy pairwise permutability conditions. First, new multi-delayed discrete matrix sine- and cosine-type functions are introduced, which generalize existing delayed discrete matrix functions. Based on the introduced matrix functions and appropriate commutativity conditions, an explicit matrix representation of the solution is derived. The importance of our results is shown by comparing them with related previous works, along with suggestions about some new open problems. Finally, an example is provided to illustrate the importance of the results. Full article

This paper investigates the pth moment exponential stability of random impulsive delayed nonlinear systems (RIDNS) with multiple periodic delayed impulses. Moreover, the continuous dynamics are described by random delay differential equations whose random disturbances are driven by second-order moment processes. Using the periodic impulsive intensity (PII), average delay time (ADT), average impulsive delay (AID), as well as the Lyapunov method, we present some pth exponential stability criteria for impulsive random delayed nonlinear systems with multiple delayed impulses. Furthermore, the criterion is unified, which is not only applicable to stable or unstable original systems but also takes into account the coexistence of stabilizing and destabilizing impulses. The periodic structure of impulses and their intensities introduces an intrinsic temporal symmetry, which plays a critical role in determining the stability behavior of the system. This symmetry-based perspective highlights the fundamental impact of regularly recurring impulsive actions on system dynamics. Several illustrated examples are given to verify the effectiveness of our results. Full article

This paper addresses challenges in speed tracking control for UAV systems equipped with variable-pitch propellers (VPPs), particularly those arising from communication delays and dynamic environmental disturbances. We propose a hybrid control strategy integrating an enhanced Smith predictor with fuzzy adaptive PID control. The Smith predictor compensates for time delays within the propulsion system, while the fuzzy PID controller dynamically adjusts for variations in UAV dynamics and external disturbances. Our approach incorporates real-time fluctuations in air-to-ground communication, encompassing both line-of-sight (LoS) and non-line-of-sight (NLoS) conditions. Theoretical analysis and numerical simulations validate the proposed architecture, demonstrating enhanced control performance, reduced delay effects, and improved robustness for real-time applications. Full article

Background: Traumatic brain injury (TBI) remains a significant contributor to global mortality and long-term neurological disability. Accurate prognostic biomarkers are crucial for enhancing prognostic accuracy and guiding personalized clinical management. Objective: This review assesses the prognostic value of arterial spin labeling (ASL), a non-invasive MRI technique, in adult and pediatric TBI, with a focus on quantitative cerebral blood flow (CBF) and arterial transit time (ATT) measures. A comprehensive literature search was conducted across PubMed, Embase, Scopus, and IEEE databases, including observational studies and clinical trials that applied ASL techniques (pCASL, PASL, VSASL, multi-PLD) in TBI patients with functional or cognitive outcomes, with outcome assessments conducted at least 3 months post-injury. Results: ASL-derived CBF and ATT parameters demonstrate potential as prognostic indicators across both acute and chronic stages of TBI. Hypoperfusion patterns correlate with worse neurocognitive outcomes, while region-specific perfusion alterations are associated with affective symptoms. Multi-delay and velocity-selective ASL sequences enhance diagnostic sensitivity in TBI with heterogeneous perfusion dynamics. Compared to conventional perfusion imaging, ASL provides absolute quantification without contrast agents, making it suitable for repeated monitoring in vulnerable populations. ASL emerges as a promising prognostic biomarker for clinical use in TBI. Conclusion: Integrating ASL into multiparametric models may improve risk stratification and guide individualized therapeutic strategies. Full article

Fractional multi-delay differential systems, as an important mathematical model, can effectively describe viscoelastic materials and non-local delay responses in ecosystem population dynamics. It has a wide and profound application background in interdisciplinary fields such as physics, biomedicine, and intelligent control. Through literature review and classification, it is evident that for the fractional multi-delay differential system, the existence and uniqueness of the solution and Ulam-Hyers stability (UHS), Ulam-Hyers-Rassias stability (UHRS) of the fractional multi-delay differential system are rarely studied by using the multi-delayed perturbation of two parameter Mittag-Leffler typematrix function. In this paper, we first establish the existence and uniqueness of the solution for the Riemann-Liouville fractional multi-delay differential system on finite intervals using the Banach and Schauder fixed point theorems. Second, we demonstrate the existence and uniqueness of the solution for the system on the unbounded intervals in the weighted function space. Furthermore, we investigate UHS and UHRS for the nonlinear fractional multi-delay differential system in unbounded intervals. Finally, numerical examples are provided to validate the key theoretical results. Full article

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. Full article

Vector-borne diseases, being one of the most difficult infectious diseases to understand, model, and control, account for a large proportion of human infectious diseases. In the current transmission process of infectious diseases, the latent period of pathogens in vivo, the influence of media coverage, and the presence of awareness on the spread and control of diseases are important factors that cannot be ignored. Based on this, a novel vector-borne disease model with latent delay and media coverage delay is proposed to discuss the impact of these factors. First, the global existence and ultimate boundedness of solutions for this model are obtained. Further, the exact expressions for the basic reproduction number are given, from which the existence and local stability of the disease-free and endemic equilibria are analyzed. Moreover, using the delay as a bifurcation parameter, we also discuss the existence, direction, and stability of the Hopf bifurcation. Finally, some numerical examples are carried out to explain the main theoretical results and discuss the impacts of the main parameters of this model on the transmission of vector-borne disease. Full article

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution $x\left(\mathrm{s}\right)$ to its corresponding function $z\left(\mathrm{s}\right)$ and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations. Full article

In this study, we aimed to characterize the nonlinear and multidelayed effects of multiple meteorological drivers on human respiratory syncytial virus (HRSV) infection epidemics in Japan. The prefecture-specific weekly time-series of the number of newly confirmed HRSV infection cases and multiple meteorological variables were collected for 47 Japanese prefectures from 1 January 2014 to 31 December 2019. We combined standard time-series generalized linear models with distributed lag nonlinear models to determine the exposure–lag–response association between the incidence relative risks (IRRs) of HRSV infection and its meteorological drivers. Pooling the 2-week cumulative estimates showed that overall high ambient temperatures (22.7 °C at the 75th percentile compared to 16.3 °C) and high relative humidity (76.4% at the 75th percentile compared to 70.4%) were associated with higher HRSV infection incidence (IRR for ambient temperature 1.068, 95% confidence interval [CI], 1.056–1.079; IRR for relative humidity 1.045, 95% CI, 1.032–1.059). Precipitation revealed a positive association trend, and for wind speed, clear evidence of a negative association was found. Our findings provide a basic picture of the seasonality of HRSV transmission and its nonlinear association with multiple meteorological drivers in the pre-HRSV-vaccination and pre-coronavirus disease 2019 (COVID-19) era in Japan. Full article

This study discusses the global asymptotical synchronization of fractional-order multi-delay coupled neural networks (FMCNNs) via hybrid control schemes. In addition to internal delays and different coupling delays, more importantly, multi-link complicated structures are introduced into our model. Unlike most existing works, the synchronization target is not the special solution of an isolated node, and a more universally accepted synchronization goal involving the average neuron states is introduced. A generalized multi-delay impulsive comparison principle with fractional order is given to solve the difficulties resulting from different delays and multi-link structures. To reduce control costs, a pinned node strategy based on the principle of statistical sorting is provided, and then a new hybrid impulsive pinning control method is established. Based on fractional-order impulsive inequalities, Laplace transforms, and fractional order stability theory, novel synchronization criteria are derived to guarantee the asymptotical synchronization of the considered FMCNN. The derived theoretical results can effectively extend the existing achievements for fractional-order neural networks with a multi-link nature. Full article

Measurements of cerebrovascular reactivity (CVR) are essential for treatment decisions in moyamoya vasculopathy (MMV). Since MMV patients are often young or cognitively impaired, anesthesia is commonly used to limit motion artifacts. Our aim was to investigate the effect of anesthesia on the CVR in pediatric MMV. We compared the CVR with multidelay-ASL and BOLD MRI, using acetazolamide as a vascular stimulus, in all awake and anesthesia pediatric MMV scans at our institution. Since a heterogeneity in disease and treatment influences the CVR, we focused on the (unaffected) cerebellum. Ten awake and nine anesthetized patients were included. The post-acetazolamide CBF and ASL-CVR were significantly lower in anesthesia patients (47.1 ± 15.4 vs. 61.4 ± 12.1, p = 0.04; 12.3 ± 8.4 vs. 23.7 ± 12.2 mL/100 g/min, p = 0.03, respectively). The final BOLD-CVR increase (0.39 ± 0.58 vs. 3.6 ± 1.2% BOLD-change (mean/SD), p < 0.0001), maximum slope of increase (0.0050 ± 0.0040%/s vs. 0.017 ± 0.0059%, p < 0.0001), and time to maximum BOLD-increase (~463 ± 136 and ~697 ± 144 s, p = 0.0028) were all significantly lower in the anesthesia group. We conclude that the response to acetazolamide is distinctively different between awake and anesthetized MMV patients, and we hypothesize that these findings can also apply to other diseases and methods of measuring CVR under anesthesia. Considering that treatment decisions heavily depend on CVR status, caution is warranted when assessing CVR under anesthesia. Full article

This article addresses the issue of drive–response synchronization in fractional-order multi-link memristive neural networks (FMMNN) with multiple delays, under hybrid impulsive feedback control. To address the impact of multiple delays on system synchronization, an extended fractional-order delayed comparison principle incorporating impulses is established. By leveraging Laplace transform, Mittag–Leffler functions, the generalized comparison principle, and hybrid impulsive feedback control schemes, several new sufficient conditions are derived to ensure synchronization in the addressed FMMNN. Unlike existing studies on fractional-order single-link memristor-based systems, our response network is a multi-link model that considers impulsive effects. Notably, the impulsive gains ${\alpha }_i$ are not limited to a small interval, thus expanding the application range of our approach (${\alpha }_i\in (-2,0)\cup (-\infty ,-2)\cup (0,+\infty )$). This feature allows one to choose impulsive gains and corresponding impulsive intervals that are appropriate for the system environment and control requirements. The theoretical results obtained in this study contribute to expanding the relevant theoretical achievements of fractional-order neural networks incorporating memristive characteristics. Full article

This study aims to investigate the asymptotic behavior of a class of third-order delay differential equations. Here, we consider an equation with a middle term and several delays. We obtain an iterative relationship between the positive solution of the studied equation and the corresponding function. Using this new relationship, we derive new criteria that ensure that all non-oscillatory solutions converge to zero. The new findings are an extension and expansion of relevant findings in the literature. We apply our results to a special case of the equation under study to clarify the importance of the new criteria. Full article

The investigation of dynamic behaviors of inertial neural networks depicted by second-order delayed differential equations has received considerable attention. Substantial research has been performed on the transformed first-order differential equations using traditional variable substitution. However, there are few studies on bifurcation dynamics using direct analysis. In this paper, a multi-delay Hopfield neural system with inertial couplings is considered. The perturbation scheme and non-reduced order technique are firstly combined into studying multi-delay induced Hopf–Hopf singularity. This combination avoids tedious computation and overcomes the disadvantages of the traditional variable-substitution reduced-order method. In the neighbor of Hopf–Hopf interaction points, interesting dynamics are found on the plane of self-connected delay and coupled delay. Multiple delays can induce the switching of stable periodic oscillation and periodic coexistence. The explicit expressions of periodic solutions are obtained. The validity of theoretical results is shown through consistency with numerical simulations. Full article