Stability Conditions Research Articles

Analyses of the SIR Epidemic Model Including Treatment and Immigration

This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete-time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points in the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of flip bifurcation. A feedback control strategy is applied to control the chaos occurring in the system after a certain period of time. We also perform numerical simulations to support analytical results. We do all these analyses for models with and without immigration and show the effect of immigration on dynamics.

The Collapse of the Vaults of the Ambato Matriz Church in the 1949 Earthquake: A Response with a Technical Approach

This research examines the structural behavior of the central vault of the Matriz church that collapsed during the 1949 earthquake in Ambato, Ecuador. Following the disaster, the church and Episcopal Palace were demolished. The central vault lacked buttresses and had large cracks two years before the collapse. A study was conducted using graphic restitution and the theory of limit analysis of structures to analyze the mechanical behavior of the central vault. The aim was to provide a technical explanation for the cause of the collapse beyond the impact of the earthquake. The limit analysis of structures is a tool that determines the technical stability conditions of a masonry structure using graphic statics. In this case, the respective checks of the structural behavior could be made, concluding that the structural ensemble of the central vault was unstable and could have collapsed at any moment, not necessarily due to an earthquake. The article is based on the research project “Architectural analysis of the central nucleus of Ambato between 1895 and 1949: styles, types, techniques, losses, and continuities”, which was conducted at the Universidad Técnica de Ambato, Ecuador, from 2021 to 2023.

Vacuum stability in the one-loop approximation of a 331 model

In this study, we analyze the vacuum stability of the economical 331 model at the one-loop level using the renormalization group equations and a single-scale renormalization method. By integrating these equations, we determine stability conditions up to the Planck scale, incorporating constraints from recent experimental data on new Higgs-like bosons, charged scalars, and charged and neutral gauge bosons. Our analysis uncovers intriguing relations between the mass of the heaviest scalar and the masses of exotic quarks, in order to ensure stability of the model up to the Planck scale. For the 331 energy scale used in this work, 18 TeV, we find an upper bound on the heaviest quark mass of the model, which is not so distant from future LHC runs, serving as bounds to be searched. Additionally, we explore relations between the scalar couplings coming stability and perturbativity conditions. These impose unprecedented constraints on the economical 331 model.

Unveiling Agricultural Shifts through Stakeholder Interactions and Strategic Dynamics in Green Rice Production

This study explores the strategic interactions among the government, growers, and the public within the context of green rice production, employing an evolutionary game theory framework. Recognizing the intricate dynamics of agricultural sustainability, we construct a three-party evolutionary game model to investigate the strategic decision-making processes and stability conditions of each stakeholder. The model assesses how various strategies evolve under the influence of economic incentives, regulatory measures, and public engagement. Through analytical and numerical methods, including stability analysis and MATLAB 2020b simulations, we identify the Evolutionarily Stable Strategies (ESS) that signify sustainable practices in green rice production. The results reveal that as government incentives for green production increase and fines for non-green practices are enforced, the likelihood of growers adopting sustainable practices significantly rises. Furthermore, the strategic enhancement of economic incentives and reputational factors not only bolsters governmental regulatory commitment but also reduces the necessity for public supervision, demonstrating a systemic shift towards self-regulation and market-driven sustainability. The simulations demonstrate the system’s evolution towards a stable state where governmental regulation is fully enforced, growers adopt green production universally, and public supervision becomes redundant. The findings underscore the importance of designing policy interventions that harmonize economic and environmental objectives, suggesting that well-structured incentives and regulatory measures can catalyze the transition towards sustainable agricultural practices. Additionally, our study highlights the pivotal role of establishing effective incentive structures that ensure the economic benefits of green production outweigh the costs, facilitating an autonomous regulatory system. This study contributes to the understanding of how strategic interactions shaped by policy and market forces can foster agricultural sustainability.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.

Stabilization of micaceous residual soil with industrial and agricultural byproducts: Perspectives from hydrophobicity, water stability, and durability enhancement

Micaceous residual soil is prevalent in the tropical regions of southern China. However, it is generally deemed unsuitable as a construction material in earthen structures due to its inferior engineering properties. Despite previous research into stabilizing micaceous soils, there remains an urgent demand for sustainable alternatives to traditional stabilizers to achieve circularity. Furthermore, uncertainties regarding the long-term performance of stabilized soils under hydraulic conditions complicated their use in flood-susceptible areas. To provide a sustainable and low-cost solution for creating stabilized soil for earthen structures in waterlogged regions, this study explores the impact of coir fiber and fly ash, agricultural and industrial byproducts, on the hydrophobicity, durability, and water stability of micaceous residual soil from Hainan, China. The study commenced with the preliminary mechanical tests to ascertain the optimal dosage of coir fiber and fly ash, which were determined to be 1% and 15%, respectively. Then, hydrophobicity, durability, and disintegration tests are conducted on fiber-reinforced fly-ash-treated soil under various stabilization conditions. The microstructural evolution of the soil fabric in response to the stabilization process was meticulously traced using scanning electron microscopy and energy-dispersive spectroscopy. Results indicated that the addition of fly ash could impart severe and persistent water repellency to the studied soil, with the contact angle improving from 16.7° to 102.9°, and the water drop penetration time significantly extending from 3.6 s to approximately 600 s. While incorporating coir fibers into the cemented soil presented negligible improvement on soil hydrophobicity, it markedly enhanced the soil’s durability, mitigated moisture-related deterioration and decelerated disintegration. Notably, the strength residual ratio of fiber-reinforced cemented sample maintained higher than 90% even after 20-day water immersion, and the disintegration rate decreased by 57% compared to unreinforced sample. Microstructural analysis revealed that bonding, friction, and interlocking among fibers, hydration products, and soil particles are the main contributors to the stable and robust matrix, ensuring improved mechanical behavior and longevity of micaceous residual soil. This study provides an innovative method for utilizing waste byproducts in stabilizing micaceous residual soil, as a viable option for earthworks in rain-soaked or flood-prone areas.

Stability analysis of discrete-time systems with arbitrary delay kernels based on kernel-related summation inequality and model transformation

In the existing papers considering the stability analysis of discrete-time systems with distributed delays via the Lyapunov-Krasovskii functional (LKF) method, the delay kernels are normally restricted to be non-negative. In this paper, we aim to remove such a restriction and deal with the stability analysis of systems with arbitrary delay kernels. For this purpose, a kernel-related summation inequality is first constructed. Then, a stability condition is derived based on the proposed inequality and a model transformation. Finally, two numerical examples are presented to show that the proposed stability condition not only has a wider scope of application and is less conservative than the existing ones.

Rational design of the aerodynamic rudder structure taking into account strength, rigidity and aeroelastic stability

The paper considers a design process of an aerodynamic rudder, which structure comprises the skin of constant thickness, a load-bearing structure and a trimmed nose that plays the role of an anti-flutter balancer. The aim of the work is to set and solve the design problem of a rational structural and technological solution of the rudder that meets the requirements of strength, rigidity, aeroelastic stability and minimum mass. To solve this problem, a design algorithm for the rudder, using topological and parametric optimization, is proposed. The main parameters of the design area and the trimmed nose required for topological optimization are determined. The ANSYS Workbench software package was used for the finite element analysis and topological optimization. Based on the results of optimization, post-processing was carried out. A structural and technological solution, that combines structural layouts with constant and variable width of the trimmed nose, was proposed. An analysis of the stress-strain state was carried out, and it was found that the designed structure meets the strength requirements for the given design case. A scheme for solving the parametric optimization problem of the rudder under the condition of aeroelastic stability is proposed. Within the framework of solving this problem, a flutter study was conducted, using a multi-mode model, which makes it possible to study the rudder and body-rudder flutter forms of an unmanned aerial vehicle (UAV) equipped with aerodynamic rudders. The results of the flutter study for the design mode of the UAV flight are obtained in the form of dependencies of the critical flutter velocity and frequency on the average width of the trimmed nose. The analysis of these dependencies allowed us to derive the optimal values of the trimmed nose parameters from the minimum weight condition for two rudder configurations: with a constant and variable width of the trimmed nose.

Multi‐agent behavioral strategy game and synergy evolution path of the retired power battery recycling system

Multi‐agent behavioral strategy game and synergy evolution path of the retired power battery recycling system

Unified Sufficient Conditions for Predefined-Time Stability of Non-Linear Systems and Its Standard Controller Design

This paper presents a unified Lyapunov-based predefined-time stability theorem that includes three sufficient conditions. The standard theoretical analysis method for achieving predefined-time stability of non-linear systems using this theorem is provided within the framework of Lyapunov theory. The developed Lyapunov-based theorem facilitates the establishment of equivalence between the existing Lyapunov theorems concerning predefined-time stability. Furthermore, when the presented sufficient conditions are relaxed, the predefined-time stability conclusion for non-linear systems degenerates into a finite-time one. Consequently, a standard non-singular sliding mode control framework based on the unified Lyapunov-based theorem is developed for a Lagrangian system to ensure its predefined-time stability. Exemplary numerical simulation results are subsequently given, in order to illustrate the convergence behavior of the system states and confirm that the controlled systems are predefined-time stable.

Effects of stochastic perturbations on a phytoplankton allelopathy competitive system

In this paper, we investigate stochastic models of two species competitive phytoplankton system with allelopathic interaction. We construct stochastic models from deterministic models by introducing three different stochastic perturbations to the equations. For the first model, we prove that this model is asymptotically stable in probability at three different equilibrium points. It is also shown that the system is positively recurrent under some conditions. For the second model, we study the extinction, existence of positive recurrence and global asymptotic stability under some sufficient conditions. For the last system, almost sufficient and necessary conditions for global asymptotic stability, the existence of positive recurrence and extinction of each population are established. In addition, using a suitable stochastic Lyapunov method, we prove that there is a unique solution to three models, we also discuss the ultimate boundedness of the three stochastic systems. Moreover, some numerical simulations are introduced to illustrate our mathematical results. We show that stochastic models still retain the desirable stability of their deterministic counterparts if stochastic perturbations are relatively small.

Religious Moderation Realizes Harmonization of The Malay Islamic Community in South Sumatra

This study aims to examine the perspective of the Malay Islamic community on religious moderation in South Sumatra. In the context of increasing globalization, religious moderation is becoming an important and relevant issue, especially in the South Sumatra region which has a significant Malay Islamic population. This research uses quantitative methods with survey methods with stakeholders from various walks of life, including religious leaders, youth, and Malay communities. The results of the study show First, that there is general agreement that religious moderation in South Sumatra is expected to increase tolerance and unity among religious communities. However, there are also different perceptions, where some feel that religious moderation can threaten their traditional values and cultural identity. Second, the results of this study also found that the understanding of religious moderation in South Sumatra is strongly influenced by the local social, economic, and political context. The contribution of this research lies in a deeper understanding of the Malay Islamic community's perspective on religious moderation in South Sumatra. Third, the results of this study show the importance of strengthening strong local identities to support community participation in stable democratic processes and efforts to create a harmonious and inclusive environment in the region. Fourth, the results of this study also show that dialogue between religious communities and religious groups, can build better understanding between each other, reduce tensions, and create more solid conditions for democratic stability.

Real-time time-varying economic nonlinear model predictive control for wind turbines

Economic nonlinear model predictive control is a great choice to tackle the control issues appearing in the current wind energy industry. In this paper, instead of generator power, aerodynamic power is employed in the economic cost function to establish the required conditions of stability and convergence of the economic performance, such as turnpike and problem convexity. However, since aerodynamic power depends on time-varying wind speed, conventional time-invariant economic nonlinear model predictive controllers cannot guarantee the stability and convergence of economic performance. This paper proposes a new time-varying economic nonlinear model predictive controller for wind turbine control that considers an economic trajectory, instead of a steady-state, in its optimization problem. The proposed time-varying economic cost function directly considers aerodynamic power, the activity of pitch angle and generator torque, and fatigue loads on the shaft and tower. Therefore, this controller can maximize power extraction and reduce fatigue load on the tower, drivetrain, and actuators. Furthermore, a fast-parallel Newton-type method is used to implement the proposed controller in actual wind turbines. An accurate aeroelastic model is used to validate the performance of the proposed control scheme. The proposed controller is also compared with two tracking nonlinear model predictive controllers, the baseline controller, and a newly developed method, under fatigue and extreme load scenarios in the presence and absence of uncertainty. The simulation results show the superior economic performance of the proposed approach. Moreover, the real-time results verify the computational speed that the proposed controller requires to deploy actual wind turbines.

Quantised adaptive consensus control of heterogeneous nonlinear multi-agent systems under external disturbance

This paper is primarily devoted to the distributed consensus tracking control for heterogeneous nonlinear multi-agent systems (MASs) with a directed communication topology. Taking the considered heterogeneous nonlinear MASs own unknown nonlinear term and quantised input signals, the adaptive radial basis function neural networks (RBFNNs)-based approximator is utilised to tackle these interesting challenges. Next, considering the boundness of disturbances, the upper bound of time-varying disturbance is utilised in the controller design. Then, a distributed dynamic compensator is developed to complete coordination task, which only requires to exchange output information via the communication network. In addition, the compensator transforms the adaptive output consensus problem into asymptotic tracking problem, without needing extra stability conditions. Finally, by means of the Lyapunov stability theory, the satisfying result of the consensus error converging to zero asymptotically can be obtained. Through simulations, the effectiveness of the developed protocol is illustrated.

Feedback stabilization of probabilistic finite state machines based on deep Q-network.

As an important mathematical model, the finite state machine (FSM) has been used in many fields, such as manufacturing system, health care, and so on. This paper analyzes the current development status of FSMs. It is pointed out that the traditional methods are often inconvenient for analysis and design, or encounter high computational complexity problems when studying FSMs. The deep Q-network (DQN) technique, which is a model-free optimization method, is introduced to solve the stabilization problem of probabilistic finite state machines (PFSMs). In order to better understand the technique, some preliminaries, including Markov decision process, ϵ-greedy strategy, DQN, and so on, are recalled. First, a necessary and sufficient stabilizability condition for PFSMs is derived. Next, the feedback stabilization problem of PFSMs is transformed into an optimization problem. Finally, by using the stabilizability condition and deep Q-network, an algorithm for solving the optimization problem (equivalently, computing a state feedback stabilizer) is provided. Compared with the traditional Q learning, DQN avoids the limited capacity problem. So our method can deal with high-dimensional complex systems efficiently. The effectiveness of our method is further demonstrated through an illustrative example.

The BAR Approach for Multiclass Queueing Networks with SBP Service Policies

The basic adjoint relationship (BAR) approach is an analysis technique based on the stationary equation of a Markov process. This approach was introduced to study heavy-traffic, steady-state convergence of generalized Jackson networks in which each service station has a single job class. We extend it to multiclass queueing networks operating under static-buffer-priority (SBP) service disciplines. Our extension makes a connection with Palm distributions that allows one to attack a difficulty arising from queue-length truncation, which appears to be unavoidable in the multiclass setting. For multiclass queueing networks operating under SBP service disciplines, our BAR approach provides an alternative to the “interchange of limits” approach that has dominated the literature in the last twenty years. The BAR approach can produce sharp results and allows one to establish steady-state convergence under three additional conditions: stability, state space collapse (SSC) and a certain matrix being “tight.” These three conditions do not appear to depend on the interarrival and service-time distributions beyond their means, and their verification can be studied as three separate modules. In particular, they can be studied in a simpler, continuous-time Markov chain setting when all distributions are exponential. As an example, these three conditions are shown to hold in reentrant lines operating under last-buffer-first-serve discipline. In a two-station, five-class reentrant line, under the heavy-traffic condition, the tight-matrix condition implies both the stability condition and the SSC condition. Whether such a relationship holds generally is an open problem.

Molecular dynamics exploration of the temperature-dependent elastic, mechanical, and anisotropic properties of hcp ruthenium

Molecular dynamics calculations were performed for the hitherto unclarified temperature-dependent elastic, mechanical, and anisotropic properties of the hexagonal closed pack (hcp) ruthenium (Ru) between 0 and 1200 K. All elastic stiffness constants were found to decrease with increasing temperature. Under the examined temperature range, hcp Ru obeys Born stability conditions. Further, both Pugh ratio analyses and calculated Poisson ratio values mutually suggest the brittle character of hcp Ru between 0 and 1200 K. The intricate hardness behavior of hcp Ru was also obtained and discussed throughout the work. For the considered temperature range, hcp Ru exhibits apparent elastic anisotropy that exponentially increases with increasing temperature. Moreover, presently obtained ground state (T = 0 K and P = 0 GPa) theoretical data for hcp Ru agree well with the former experimental and theoretical data. The present findings on the temperature-dependent characteristics of this metal may further inspire future applied works.Graphical abstract

Numerical modeling of mixed convective nanofluid flow with fractal stochastic heat and mass transfer using finite differences

This study presents the first comprehensive numerical simulation of heat and mass transfer in fractal-like mixed convective nanofluid flows. The flow of non-Newtonian nanofluids over flat and oscillating sheets is modelled mathematically, and a finite difference scheme is used to solve this model. The two-stage scheme can tackle fractal and fractal stochastic mathematical models of partial differential equations. The consistency in the mean square is proved, and Fourier series stability analysis is adopted to find stability conditions for fractal stochastic partial differential equation. The scheme is applied to solve the unsteady Casson nanofluid flow over the flat and oscillatory sheet, which affects thermal radiation, heat source, and chemical reaction. The existence of the solution is also provided for the Navier-Stokes equation of the considered flow model using fractal time derivative. The graph illustrates that the proposed fractal technique achieves faster convergence than the Crank-Nicolson approach. Applications in energy systems, materials science, and environmental engineering are just a few of the domains that could benefit from a better understanding of mixed convective nanofluid flows with fractal features, and that is what this research study hopes to accomplish. Scientists and engineers may better develop efficient and environmentally friendly systems by simulating and analyzing these complicated processes with the suggested finite difference technique.

Research on dynamic stability of rolling missiles employing direct/aerodynamic force compound control

The direct/aerodynamic force compound control can enhance the maneuverability and response characteristics of missiles, and the dynamic stabilization is the precondition of normal operation for rolling missiles. Aiming at the stability problem caused by the cross-coupling effect of rolling missiles employing direct/aerodynamic force compound control, proposing a typical topological control system structure described by the complex coefficient theory, and deducing the dynamic stability conditions. Firstly, the mathematic model is established based on the kinematics and dynamics theories of rotating airframes and the direct/aerodynamic force compound control mechanism. Then, a three-loop autopilot and the direct/aerodynamic force ratio distribution method are designed to establish the complex summation model of the compound control system by selecting suitable complex variables. Furthermore, deducing the dynamic stability conditions and verifying them by numerical simulations. Finally, the stable regions of the rolling missile in different cases are obtained and found to be influenced by many factors, such as parameters of the autopilot, hybrid force distribution proportion and rolling rate. The derived dynamic stability criterion is effective for evaluating the stability of rolling missiles employing direct/aerodynamic force compound control and the research method used in this paper can provide reference for the stability study of strongly coupled nonlinear systems.

State Estimation for Recurrent Neural Networks With Intermittent Transmission.

This work addresses the state estimation problem for recurrent neural networks over capacity-constrained communication channels. The intermittent transmission protocol is used to reduce the communication load, where a stochastic variable with a given distribution is used to describe the transmission interval. A corresponding transmission interval-dependent estimator is designed, and an estimation error system based on it is also derived, whose mean-square stability is proved by constructing an interval-dependent function. By analyzing the performance in each transmission interval, sufficient conditions of the mean-square stability and the strict (Q,S,R) - γ -dissipativity are established for the estimation error system. Finally, the correctness and the superiority of the developed result are illustrated by a numerical example.