Stability Matrix Research Articles

Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation

In this paper, we study the asymptotic and transient dynamics of a predator–prey model with square root functional responses and random perturbation. Firstly, the mean square stability matrix is obtained from the stability theory of stochastic systems, and three stability indexes (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the ecosystem response to stochastic disturbances are calculated. We find that: (1) no matter which population is disturbed, increasing the intensity of disturbance improves the ability of the system leaves steady state and thus decreases the stability. The root-mean-square amplification envelope rises with increasing disturbance intensity, (2) the system is more sensitive to the disturbance of the predator than disturbance to prey, (3) ρmax and tmax are important indicators, which represent the intensity and time of maximum amplification by disturbance. These findings are helpful for managers to take corresponding management measures to reduce the disturbances, especially for predators, thereby avoiding the possible change of the structure and functions of the ecosystem.

Second-Order Hybrid Consensus of Multi-Agent Systems With Matrix-Weighted Networks

This article considers a hybrid consensus in the context of second-order multi-agent systems with matrix-weighted networks. A matrix-weighted hybrid consensus controller is built upon the sampled-data method in continuous-time subsystem. For the cases of undirected graph and directed graph, some sufficient and necessary conditions, which depend on the sampling period, coupling gains and the eigenvalues of Laplacian matrix, are derived with the assistance of stability theory and matrix theory. Finally, through simulation comparison, the validity of the obtained results is demonstrated.

Particle Technology in the Formulation and Fabrication of Thermal Energy Storage Materials

AbstractThis article reviews the state of the art of the formulation and fabrication of sensible, latent, and thermochemical thermal energy storage (TES) materials with special focus on the role of particle technology in enhancing the performance of these materials. Molten salt‐based sensible TES materials have been intensively studied, particularly the use of doped nanoparticles for enhancing specific heat capacity and thermal conductivity. For latent TES, the inclusion of property enhancers is among the most effective approaches to address the low thermal conductivity and supercooling issues of phase change materials (PCMs), whereas the encapsulation of PCMs and structurally stabilized composite PCMs are the favorable methods to address leakage and chemical incompatibility challenges. Thermochemical TES materials are often incorporated with an inert or an active host matrix for structural stabilization.

Robust Controller Numerical Design for Reinforced Concrete Structures Under Seismic Excitation Conditions

The article discusses driver optimization design issues that combine the evolution of artificial intelligence of the bat optimization algorithm with fuzzy drivers to enable practical applications in construction. The designation of system controllers includes various subsections such as initial system parameters, EB optimization algorithm, cloud controllers, stability analysis, and excitation sensors. The advantage of this design is the integrated H2 / H output of a robust strategy for certain systems with continuous and polyhedral uncertainties f or. The asymptote was obtained by adjusting the design parameters with the help of correction criteria. Numerical verification of the time and frequency domain shows the new system design to accurately predict and control the structural displacement reactions required to actively control each model structure . The Genetic Algorithm Test technique uses the Hurwitz Matrix Functional Structure hierarchy for hierarchical conditions and measures of exacerbation of effect. This article proposes any type of dynamic controller to obtain the optimal power structure required for active control of nonlinear structures. This method has shown favorable results in the resolutions of closed systems.

Sextic tensor model in rank 3 at next-to-leading order

We compute the four-loop beta functions of short and long-range multi-scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a U(N)3 symmetry and study the renormalization group at next-to-leading order in N and small ϵ. In the short-range case, ϵ is the deviation from the critical dimension while it is the deviation from the critical scaling of the free propagator in the long-range case. This allows us to find the 1/N corrections to the rank-3 sextic tensor model of [1]. In the short-range case, we still find a non-trivial real IR stable fixed point, with a diagonalizable stability matrix. All couplings, except for the so-called wheel coupling, have terms of order ϵ0 at leading and next-to-leading order, which makes this fixed point different from the other melonic fixed points found in quartic models. In the long-range case, the corrections to the fixed point are instead not perturbative in ϵ and hence unreliable; we thus find no precursor of the large-N fixed point.

Simultaneous quantification of multiple active components of the ginkgo ketoester tablet when combined with donepezil in four biological matrices from an Alzheimer’s animal model: Evaluation of drug distribution patterns in vivo

Ginkgo ketoester tablets (GT) and donepezil are clinically used in combination to treat Alzheimer’s disease (AD). This study aimed to investigate the anti-dementia effects of two drugs alone and in combination by monitoring the distribution patterns of their active components in different biological matrices. A practical analytical method was developed for simultaneously quantifying 38 active compounds in different matrices at trace levels using ultra-performance liquid chromatography coupled with triple-quadrupole linear ion-trap tandem mass spectrometry (UHPLC-MS2). Under optimized conditions, good chromatographic separation of the 38 target compounds was achieved within 14 min, with acceptable linearity, limits of detections and quantifications, precision, stability, and extraction recovery and matrix effects. The developed analytical method quantified the 38 active components in the brain, plasma, intestine, and intestinal contents of AD mice treated with GT alone, donepezil alone, and a combination of the two drugs. The result showed that the combination group had enhanced anti-dementia active compounds and reduced levels of toxic compounds entering the targeted tissues. These findings support the combined use of GT and donepezil for increasing anti-dementia treatment efficiency and reducing toxicity. The proposed UHPLC-MS2 strategy could be used to monitor the levels of active compounds from different biological matrices in future studies.

LAGUERRE WAVELET METHOD FOR FRACTIONAL PREDATOR–PREY POPULATION MODEL

The adaptation of fractional calculus (FC) in biological mathematical model takes the research in the area of the public health to a new level. The fractional definitions and related mathematical tools have had a significant impact on biological models analysis. The main goal of this paper is to examine the dynamical behavior of a predator–prey model under Caputo derivative. We analyze some special results such as convergence analysis, stability and operational matrix for the proposed Caputo model. For solution of the model, we present a new numerical technique-based Laguerre wavelet. In addition, we graphically compare the numerical results obtained using Laguerre wavelets and Lagrange polynomial interpolation.

Robust subtractive stability measures for fast and exhaustive feature importance ranking and selection in generalised linear models

AbstractWe introduce the relatively new concept of subtractive lack‐of‐fit measures in the context of robust regression, in particular in generalised linear models. We devise a fast and robust feature selection framework for regression that empirically enjoys better performance than other selection methods while remaining computationally feasible when fully exhaustive methods are not. Our method builds on the concepts of model stability, subtractive lack‐of‐fit measures and repeated model identification. We demonstrate how the multiple implementations add value in a robust regression type context, in particular through utilizing a combination of robust regression coefficient and scale estimates. Through resampling, we construct a robust stability matrix, which contains multiple measures of feature importance for each variable. By constructing this stability matrix and using it to rank features based on importance, we are able to reduce the candidate model space and then perform an exhaustive search on the remaining models. We also introduce two different visualisations to better convey information held within the stability matrix; a subtractive Mosaic Probability Plot and a subtractive Variable Inclusion Plot. We demonstrate how these graphics allow for a better understanding of how variable importance changes under small alterations to the underlying data. Our framework is made available in R through the RobStabR package.

A numerical scheme for the wave simulations of the Kuramoto–Sivashinsky model via quartic-trigonometric tension B-spline

In this work, the numerical investigation of the Kuramoto–Sivashinsky model with the application of the relatively-new proposed tension B-spline function, is studied. The numerically computed scheme is conducted with the hybridizable approach using collocation method in space and time directions. The spatial discretization results in the time-dependent system of equations. Then, the system is integrated by Crank–Nicolson technique which finally generates wholly constructed space–time scheme. Therefore, numerical solution of the Kuramoto–Sivashinsky model is obtained. The stability of the numerical scheme is performed by considering the stability matrix. Then, the stable regions have been presented in terms of the eigenvalues of the linearized system. The efficiency of the computational procedure is confirmed on sample problems. These numerical experiments are also studied to demonstrate the well-known characteristics of the model equation. In particular, dynamics of shock-waves, periodic nature and turbulent flows have been illustrated. The hybrid collocation scheme have successfully generated the nonlinear wave behavior of the Kuramoto–Sivashinsky model.

Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible/Incompressible Formulation: The Full Navier–Stokes Approach versus the Boussinesq Model

This paper compares two strategies to compute buoyancy-driven flows using stabilized methods. Both formulations are based on a unified approach for solving compressible and incompressible flows, which solves the continuity, momentum, and total energy equations in a coupled entropy-consistent way. The first approach introduces the variable density thermodynamics of the liquid or gas without any artificial buoyancy terms, i.e., without applying any approximate models into the Navier–Stokes equations. Furthermore, this formulation holds for flows driven by high temperature differences. Further advantages of this formulation are seen in the fact that it conserves the total energy and it lacks the incompressibility inconsistencies due to volume changes induced by temperature variations. The second strategy uses the Boussinesq approximation to account for temperature-driven forces. This method models the thermal terms in the momentum equation through a temperature-dependent nonlinear source term. Computer examples show that the thermodynamic approach, which does not introduce any artificial terms into the Navier–Stokes equations, is conceptually simpler and, with the incompressible stabilization matrix, attains similar residual convergence with iteration count to methods based on the Boussinesq approximation. For the Boussinesq model, the SUPG and SGS methods are compared, displaying very similar computational behavior. Finally, the VMS a posteriori error estimator is applied to adapt the mesh, helping to achieve better accuracy for the same number of degrees of freedom.

Stationary Behavior of Constant Stepsize SGD Type Algorithms

Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However, constant stepsize SA algorithms do not converge to the optimal solution, but instead have a stationary distribution, which in general cannot be analytically characterized. In this work, we study the asymptotic behavior of the appropriately scaled stationary distribution, in the limit when the constant stepsize goes to zero. Specifically, we consider the following three settings: (1) SGD algorithm with a smooth and strongly convex objective, (2) linear SA algorithm involving a Hurwitz matrix, and (3) nonlinear SA algorithm involving a contractive operator. When the iterate is scaled by 1/√α, where α is the constant stepsize, we show that the limiting scaled stationary distribution is a solution of an implicit equation. Under a uniqueness assumption (which can be removed in certain settings) on this equation, we further characterize the limiting distribution as a Gaussian distribution whose covariance matrix is the unique solution of an appropriate Lyapunov equation. For SA algorithms beyond these cases, our numerical experiments suggest that unlike central limit theorem type results: (1) the scaling factor need not be 1/√α, and (2) the limiting distribution need not be Gaussian. Based on the numerical study, we come up with a heuristic formula to determine the right scaling factor, and make a connection to the Euler-Maruyama discretization scheme for approximating stochastic differential equations.

Starch as a Matrix for Incorporation and Release of Bioactive Compounds: Fundamentals and Applications.

Due to its abundance in nature and low cost, starch is one of the most relevant raw materials for replacing synthetic polymers in a number of applications. It is generally regarded as non-toxic, biocompatible, and biodegradable and, therefore, a safe option for biomedical, food, and packaging applications. In this review, we focused on studies that report the use of starch as a matrix for stabilization, incorporation, or release of bioactive compounds, and explore a wide range of applications of starch-based materials. One of the key application areas for bioactive compounds incorporated in starch matrices is the pharmaceutical industry, especially in orally disintegrating films. The packaging industry has also shown great interest in using starch films, especially those with antioxidant activity. Regarding food technology, starch can be used as a stabilizer in nanoemulsions, thus allowing the incorporation of bioactive compounds in a variety of food types. Starch also presents potential in the cosmetic industry as a delivery system. However, there are still several types of industry that could benefit from the incorporation of starch matrices with bioactive compounds, which are described in this review. In addition, the use of microbial bioactive compounds in starch matrices represents an almost unexplored field still to be investigated.

Stochastic heat equation: Numerical positivity and almost surely exponential stability

In this paper, the numerical positivity and almost surely exponential stability of the stochastic heat equation are discussed. The finite difference method and the split-step backward Euler are considered for spatial and temporal, respectively. Motivated from physical applications such as temperature, finance and so on, positivity has real significance, which is volatilized by some common numerical treatments. To this end the numerical positivity is obtained by the properties of M-matrix and the truncated random variables, which overcomes the unboundedness of the random variables. For the investigation of the almost surely exponential stability, a stochastic stability matrix is introduced, and then the stability analysis reduces to the estimation of the eigenvalues and martingales thorough a family of matrices and perturbation theorems. The stabilization ability of the multiplicative noise is verified again from a generalization of the stochastic heat equation. Finally, some numerical experiments are given to validate our numerical results.

Thermal energy storage composites with preformed expanded graphite matrix and paraffin wax for long-term cycling stability and tailored thermal properties

Harvesting solar energy, preventing hot spots in electronics, transport of temperature-sensitive materials, and capture and repurposing of thermal energy require a latent heat thermal energy storage (TES) system to store/discharge heat repeatedly. For the practical application of phase change material (PCM) composites within TES systems, reliable thermal performance throughout its operational lifetime is essential. Nevertheless, the reliability of thermal conductivity in multi-phase composites over relevant numbers (>103) of melt/freeze cycles has barely been studied, particularly for composites containing fillers for thermal conductivity enhancement. Here, we introduce a preform-type expanded graphite (EG)/paraffin wax composite possessing highly robust heat transfer and storage properties even after 10,000 melt/freeze cycles. To achieve such excellent reliability, comparative studies on the combined influence of fabrication process, particle size, EG vol%, binder amount, and compaction on both magnitude and robustness of thermal conductivity were undertaken. Our parametric study has yielded a trade-off between thermal conductivity and latent heat. Based on our modeling, 20 vol% EG approaches the case where all EG particles are well-connected thermally while 10 vol% EG is close to loosely connected fillers in the matrix. Thermal conductivity of our paraffin composites containing 20 vol% EG (25.1 W·m−1·K−1) is highest among other EG/paraffin composites without aligned EG in the literature. After 10,000 thermal cycling, negligible conductivity fading was observed for the 10 vol% EG composite, while reduction in latent heat remained within 10% for all 10, 14, 17 and 20 vol% EG samples. We anticipate this work provides insight on suitable recipe for desirable magnitude and robustness of thermal conductivity of EG/paraffin composites.

Bandwidth estimation in high mobility scenarios of MANET using NSGA-II optimized fuzzy inference system

Integration of mobility to sensor node enhanced the scalability of Ad-hoc networks. Bandwidth estimation in scenarios where nodes move randomly and frequently changes its link may depend on factors other than congestion in network traffic. The event of link failure due to the high mobility behavior of nodes in the path from source to destination is one of the dominating cause. However, in both cases, TCP’s new-Reno and its variants reduce the congestion-window size to half or 1-MSS, which can cause bandwidth underutilization in the event of a packet drop due to link failure. The proposed approach distinguishes the link failure from network congestion and estimates bandwidth based on link and path stability matrix. The contribution includes the identification of node mobility fuzziness in unicast and broadcast scenarios of IEEE 802.15.4 based MANET. The mobility-fuzziness formulation by the proposed NSGA-II optimized fuzzy-inference-system imitates the node’s mobility behavior and, in the event of packet loss, is employed to realize the path-stability metric to estimate the congestion window size. The thorough evaluation with current state-of-the-art techniques shows that the proposed path stability metric allows the estimation of congestion window size to the current congestion window in the event of a packet loss due to link failure. Improving the bandwidth utilization metric in high mobility scenarios from 53–61% for existing approaches to above 83% in proposed approach.

On the Extrapolation of Stability Derivatives to Combined Changes in Airspeed and Angles of Attack and Sideslip

The variation in stability derivatives with airspeed and angles of attack and sideslip is determined using only the dependence of the aerodynamic forces and moments on the modulus and direction of the velocity. Analytic extrapolation factors are obtained for all 12 longitudinal plus 12 lateral stability derivatives of linear decoupled motion. The extrapolation factors relate the stability derivatives for two flight conditions with different airspeeds, angles of attack (AoA), and angles of sideslip (AoS). The extrapolation formulas were validated by comparison with results of computational fluid dynamics (CFD) using Reynolds-averaged Navier–Stokes (RANS) equations. The comparison concerns the extrapolated full longitudinal–lateral stability matrix from one landing and one takeoff condition of a V-tailed aircraft, to 10 other landing and takeoff flight cases with different airspeeds, AoAs, and AoSs. Thus, 420 comparisons were made between extrapolated stability derivatives and CFD–RANS results demonstrating the achievable levels of accuracy.

Hybrid‐triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

AbstractThis paper is concerned with the issue of hybrid‐triggered scheme asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid‐triggered scheme includes time‐triggered scheme and event‐triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean‐square asymptotically stable (MSAS) and performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width‐modulation‐driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.

An application of interval type-2 fuzzy model based control system for generic aircraft

This paper presents a design application of Interval Type-2 (IT2) Takagi–Sugeno (T–S)​ Fuzzy Model Based (FMB) control system for generic aircraft. The IT2 T–S FMB flight control system consists of an IT2 T–S fuzzy model and a fuzzy controller connected in a closed-loop. The IT2 T–S​ fuzzy model is obtained by linearizing the nonlinear aircraft dynamics about various representative points (equilibrium points) of the flight envelope with some fuzzy rules. The aircraft flight envelope parameters, i.e., operating altitude and aircraft speed are characterized as premise parameters and elements of stability and control derivative matrix are identified as consequent parameters of fuzzy model. Longitudinal dynamics of X-29A research aircraft is selected for design of IT2 T–S FMB control system. To achieve the optimum design flexibility, an imperfectly matched premise and membership function dependent (MFD) stability analysis is considered. In MFD stability conditions, the information of flight envelope parameters is included to capture the nonlinearity pertaining to variation in flight conditions. The closed-loop response of IT2 T–S FMB controller is presented at trim equilibrium points by taking four initial angle of attack flight conditions. The performance analysis of designed controller is also presented and discussed in comparison with Fuzzy LQR and LQR based optimal controllers. The simulation results reveal that proposed IT2 T–S FMB controller not only stabilizes the aircraft dynamics but also provides improved transient performance as compared with Fuzzy LQR and LQR based optimal controllers. This demonstrates the utility of IT2 T–S FMB control system for aircraft/ UAV’s related application.

3D Lipidic Matrix for Incorporation and Stabilization of Biologically Active Molecules

In aqueous media, biologically active substances are usually unstable, poorly soluble compounds with low bioavailability. Incorporation of these compounds into the structure of lipid-based lyotropic liquid crystalline phase or nanoparticles can increase their solubility and subsequent bioavailability. The aim of this review is to clarify the principle of self-assembly of lipidic amphiphilic molecules in the aqueous environment, to present lipid bicontinuous cubic and hexagonal phases and their current biological application.

Stationary Behavior of Constant Stepsize SGD Type Algorithms

Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However, constant stepsize SA algorithms do not converge to the optimal solution, but instead have a stationary distribution, which in general cannot be analytically characterized. In this work, we study the asymptotic behavior of the appropriately scaled stationary distribution, in the limit when the constant stepsize goes to zero. Specifically, we consider the following three settings: (1) SGD algorithm with a smooth and strongly convex objective, (2) linear SA algorithm involving a Hurwitz matrix, and (3) nonlinear SA algorithm involving a contractive operator. When the iterate is scaled by 1/α, where α is the constant stepsize, we show that the limiting scaled stationary distribution is a solution of an implicit equation. Under a uniqueness assumption (which can be removed in certain settings) on this equation, we further characterize the limiting distribution as a Gaussian distribution whose covariance matrix is the unique solution of a suitable Lyapunov equation. For SA algorithms beyond these cases, our numerical experiments suggest that unlike central limit theorem type results: (1) the scaling factor need not be 1/α, and (2) the limiting distribution need not be Gaussian. Based on the numerical study, we come up with a heuristic formula to determine the right scaling factor, and make insightful connection to the Euler-Maruyama discretization scheme for approximating stochastic differential equations.