Global Stability Research Articles

Russia’s Declining Satellite Reconnaissance Capabilities and Its Implications for Security and International Stability

Satellite-based intelligence has played a crucial role in national security and international stability. This article explores the persistent decline in Russia’s satellite reconnaissance capabilities since the Cold War’s end, challenging hopes for recovery and highlighting systemic issues. It delves into the impact on Russia’s military actions in Ukraine, where the absence of satellites contributes to indiscriminate shelling and higher military casualties. Furthermore, it examines the repercussions on nuclear arms control and the peaceful use of space, critical for global stability. As Russia struggles with reconnaissance gaps, its pursuit of antisatellite weapons poses a threat to the principle of space for peace. This analysis aims to deepen insights into the intelligence decline during the Russia–Ukraine conflict and its potential ramifications for international stability.

Mathematical modeling and control of Covid‐19

In this paper, the author proposes and studies a mathematical model for the spread of coronavirus 2019. The effect of preventive programs on the control of disease is also considered. The basic reproduction number was computed and the results showed that forward bifurcation occured. Local and global stability of the equilibrium points of the model was studied by geometric stability method and Lyapunov function. Finally, the particular data of China which was reported for Covid‐19 were used for numerical simulation.

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.

Existence and exponential stability of a periodic solution of an infinite delay differential system with applications to Cohen–Grossberg neural networks

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincidence degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen–Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and two numerical examples to illustrate the effectiveness of some of our results.

Green finance and food production: Evidence from cities in China

In the domain of global socio-economic dynamics, the pivotal role of food production (FP) cannot be overstated. It constitutes the bedrock of fundamental human necessities while being inexorably linked with critical aspects such as economic expansion, societal equilibrium, and geopolitical interplays. The multifaceted nature of FP appears through its direct impact on macroeconomic indicators and its latent influence on international relations and policy-making. This critical nexus underscores the imperative for a comprehensive understanding and strategic management of food production processes to sustain and enhance global socio-economic stability and growth. Investigating the nexus between green finance (GF) and FP is pivotal for ensuring national security and promoting sustainable economic development. This research thus paper examines GF's impact on FP in China as outlined in the 2017 green finance policies. It employs the difference-in-differences (DID) method and analyzes a balanced panel dataset comprising 282 cities in China from 2009 to 2020. The results show that GF has an inhibitory effect on FP, and this remains valid after a range of reliability checks, including parallel trend assessments and placebo tests. Further findings of transmission mechanism analysis indicate that non-agricultural factors and financial exclusion are critical for GF's inhibitory effect on FP. Heterogeneity analyses show that GF's inhibitory effect on FP is more pronounced in the main food-producing areas, the main food-marketing areas, and cities with better infrastructure. The empirical results of this paper comprehensively illustrate GF's impact on FP and how it contributes to the achievement of food security objectives.

The role of taxation in an integrated economic-environmental model: a dynamical analysis

AbstractWe propose a model with economic and environmental domains that interact with each other. The economic sphere is described by a Solow growth model, in which productivity is not exogenous but negatively affected by the stock of pollution that stems from the production process. A regulator can charge a tax on production, and the resources collected from taxation are used to reduce pollution. The resulting model consists of a two dimensional discrete dynamical system, and we study the role of taxation from both a static and a dynamical point of view. The focus is on the determination of the conditions under which taxation has a positive effect on the environment and leads to economic growth. Moreover, we show that a suitable environmental policy can allow recovering both local and global stability of the steady states. On the contrary, we show that, if the policy is not adequate, the system can exhibit endogenous oscillating and chaotic behavior and multistability phenomena.

Modeling the Transmission Dynamics of Tuberculosis in Humans

Tuberculosis (TB) is a major threat to human health particularly in most of developing countries. In this article, we formulate and analyze a deterministic model for the transmission dynamics of pulmonary and extra-pulmonary tuberculosis. The next generation method is employed to find the basic reproduction number R0 which helps to determine whether TB clears or persists in the human population. Global stability of model equilibria is done through Lyapunov functions whereas the normalized forward sensitivity index method is adopted to determine parameters that drive tuberculosis. Analysis shows that both TB free and endemic equilibria exist. The TB free equilibrium is globally asymptotically stable whenever the basic reproduction number R0 < 1 whereas the endemic equilibrium is globally asymptotically stable whenever R0 > 1. Sensitivity analysis shows that the TB infection rate, the fraction of individuals who progress to pulmonary tuberculosis and its induced death drive TB. Numerical results indicate that when there are no interventions, susceptible humans decline significantly with time until when they are attracted to the steady state whereas latently infected, pulmonary and extra-pulmonary TB individuals increase until when they settle at the equilibrium states supporting the analytical results for existence of the endemic equilibrium. In light of these findings, we recommend treating humans infected with pulmonary TB who are carriers of the disease.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Mapping annual 10-m soybean cropland with spatiotemporal sample migration

China, as the world’s biggest soybean importer and fourth-largest producer, needs accurate mapping of its planting areas for global food supply stability. The challenge lies in gathering and collating ground survey data for different crops. We proposed a spatiotemporal migration method leveraging vegetation indices’ temporal characteristics. This method uses a feature space of six integrals from the crops’ phenological curves and a concavity-convexity index to distinguish soybean and non-soybean samples in cropland. Using a limited number of actual samples and our method, we extracted features from optical time-series images throughout the soybean growing season. The cloud and rain-affected data were supplemented with SAR data. We then used the random forest algorithm for classification. Consequently, we developed the 10-meter resolution ChinaSoybean10 maps for the ten primary soybean-producing provinces from 2019 to 2022. The map showed an overall accuracy of about 93%, aligning significantly with the statistical yearbook data, confirming its reliability. This research aids soybean growth monitoring, yield estimation, strategy development, resource management, and food scarcity mitigation, and promotes sustainable agriculture.

Vaccination games and imitation dynamics with age structure combining perceived payoffs and media information

We propose an age-structured model based on game theory to investigate the dynamics of imitation in vaccination decisions. In our model, the rate at which individuals switch vaccination strategies is proportional to the perceived payoffs and media information. We analyze the existence and local stability of equilibria and demonstrate the possibility of Hopf bifurcation. Additionally, we establish the global stability of boundary equilibria and the persistence of the disease. The theoretical results are supported by numerical simulations. This model can be applied to study vaccination behavior among individuals of different ages and infectious disease stages, providing insights for the formulation of effective public health policies.

Premixed flames in narrow heated channels of circular cross-section: Steady-state solutions, their linear stability analysis and the multiplicity of stable dynamic modes

Premixed flames in narrow heated circular channels subjected to a Poiseuille flow are investigated within the constant density model for various Lewis numbers using irreversible one-step Arrhenius kinetics. A global stability analysis of steady-state axisymmetric solutions is carried out, together with time-dependent direct numerical simulations. The analysis reveals the criteria for the appearance of oscillatory and three-dimensional cellular flame structures. The problem is also studied separately within the framework of the narrow-channel approximation.Among the results obtained, the following can be singled out as the main ones. First, the multiplicity of stable dynamic modes, oscillatory and steady-state, taking place for the same set of parameters for flames with Le<1 is demonstrated. The actual occurrence of one mode or another depends on the initial conditions. Second, the appearance of chaotic regimes is shown for flames with Le>1. The chaotic dynamics occurs in a narrow range of values of the flow rate, with Feigenbaum period-doubling cascades taking place both before and after this interval. The results of this study could be useful in the development and use of small-scale combustion devices.Novelty and significance statement: A systematic study of premixed flames in narrow heated circular channels in the presence of Poiseuille flow is carried out for various Lewis numbers using irreversible one-step Arrhenius kinetics. One of the novelties presented in the paper is the linear global stability analysis of steady state axisymmetric solutions of this problem, which has not been reported before. Also, for the first time, the existence of multiple stable dynamic modes, oscillatory and time-independent, which occurs at the same parameter values, is demonstrated for flames with Lewis number smaller than one. For flames with a Lewis number greater than one, cases with chaotic dynamics are found that manifest themselves in a narrow range of the flow rate. Finally, it is demonstrated that the Feigenbaum cycle-doubling cascade can appear before and after this interval of chaotic dynamics. Such analysis has not been reported before for this problem of flames in partially heated channels.

Wiener and Lévy processes to prevent disease outbreaks: Predictable vs stochastic analysis

The study considers stochastic behavior along with modeling, mathematical analysis, theory development, and numerical simulation of the COVID-19 virus. To evaluate current trends and make future projections regarding the basic reproduction number and infection case, we have taken the modified five-compartment SEIRD mathematical model. Since the basic reproduction number R0 is not sufficient to predict the outbreak, we applied the Itô stochastic differential equations (SDEs) along with the Weiner process and Lévy jump to investigate the nature of the disease outbreak. Since COVID-19 is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 “(SARS-CoV-2)”, that has common symptoms including fever, cough, and difficulty breathing, we have illustrated the boundedness and positivity of solutions and investigated the stability of endemic and disease-free equilibrium points. The findings show that the dynamics of disease epidemics are influenced by contact patterns. For all the models, the threshold quantity, R0 is calculated which is the key reason to prove the global and local stability analysis of disease-free equilibrium and endemic equilibrium points. Using the least squares method for data fitting, we have performed a case study on COVID-19 data in Italy for this article. A sensitivity analysis is part of our investigation to find important factors. This paper investigates a stochastic epidemic model (SDE) using Lévy jumps and Weiner processes. Local and global stability in a stochastic setting are examined in the analysis. To view the analytical study, a multitude of numerical results are achieved. The study is important to comprehend the stochastic behavior of the virus in the contagious model in order to prevent similar disease outbreaks in the future.

Spatiotemporal dynamics of prey-predator model incorporating Holling-type II functional response with fear and its carryover effects.

The recent focus in the fields of biology and ecology has centered on the significant attention given to the mathematical modeling and analyzing the spatiotemporal population distribution among species engaged in interactions. This paper explores the dynamics of the temporal and spatiotemporal delayed Bazykin-type prey-predator model, incorporating fear and its carryover effect. In our model, we incorporated a functional response of the Holling-type II. In the temporal model, a detailed dynamic analysis was carried out, investigating the positivity and boundedness of solutions, establishing the uniqueness and existence of positive interior equilibria, and examining both local and global stability. Additionally, we explored the presence of saddle-node, transcritical, and Hopf bifurcations varying attack rate parameter. The delayed system shows highly periodic behavior. Additionally, for the spatiotemporal model, we provide a complete analysis of local and global stability, and we derive the conditions for the existence of Turing instability for both self-diffusion and cross-diffusion, respectively. The two-dimensional diffusive model is further discussed, highlighting various Turing patterns, including holes, stripes, and hot and cold spots, along with their biological significance. Numerical simulations are executed to validate the analytical findings in both temporal and spatiotemporal models.

Kalman filter based on a fractional discrete-time stochastic augmented CoVid-19 model

In this paper, we study the dynamics of the CoVid-19 outbreak in Semarang, Indonesia, using a fractional CoVid-19 model. We first determine the effects of the isolation rate ∊ and infection rate β on the reproduction number R0 and infected number V. We find that R0 is directly proportional to β and inversely proportional to ∊. For V, the effect of physical distancing is not as significant as changing ∊. As ∊ increases, V decreases, the number of susceptible individuals increases, the number of quarantined individuals decreases sharply, and the number of recovered individuals decreases. Moreover, the effect of vaccination is also considered. The combination of physical distancing, isolation, and vaccination has a significant impact on reducing the number of infected individuals. Analysis of dynamical systems allows us to understand the characteristics of our model, such as its boundedness and non-negativity, the existence of equilibrium points, the existence and uniqueness of solutions, and the local and global stability. To validate our fractional CoVid-19 model, we introduce the fractional extended Kalman filter (FracEKF) as a prediction method and compare the results against reported CoVid-19 data. FracEKF is a modified version of the basic extended Kalman filter with a time-fractional memory effect. The prediction results illustrate the accuracy of this model in terms of the root mean square error (RMSE), normalized root mean square error (NRMSE), and mean absolute percentage error (MAPE) for each fractional-order. Varying ∊ reproduces the trends observed in the reported data for the number of infected individuals, i.e., when ∊ increases, the infected number decreases. Moreover, a higher fractional-order results in higher model accuracy. Furthermore, higher values of the process noise Qf give smaller errors, whereas higher values of the observation noise Rf produce higher errors. Qf and the fractional-order α are inversely proportional to RMSE,NRMSE, and MAPE, whereas Rf is directly proportional to RMSE,NRMSE, and MAPE.

Fault-Tolerant Control of Stochastic High-Order Fully Actuated Systems.

In recent years, high-order fully actuated (HOFA) systems, founded by Prof. GR Duan, have recorded rapid progress for deterministic systems. However, the control issue of stochastic fully actuated systems is still an open problem. This study develops a novel stochastic HOFA system model that complements the existing HOFA methodology. Notably, stochastic signals can be considered in the proposed model, different from the case in the deterministic model. By adopting a high-order operator, equivalent control and stabilization control laws are realized to guarantee the global asymptotic stability in probability of the closed-loop system. For the system with sensor gain faults, an observer-based fault-tolerant control law is designed. Finally, the simulation results validate the effectiveness of the proposed control schemes.

Cadmium(II) adsorption by recyclable Zeolite-Loaded Hydrogel: Extension to the removal of Cadmium(II) from contaminated soil

Excessive cadmium(II) (Cd(II)) in soil has gravely jeopardized global ecosystem stability and human health. The removal of Cd(II) is a permanent cure to remediate Cd(II)-contaminated soil. Herein, a recyclable removal material, zeolite@cellulose-poly(acrylamide) hydrogel (Z@CA) was developed. Batch adsorption experiments and characterisations (SEM-EDS, FTIR, XRD, and XPS) were conducted to explore the adsorption capacity and mechanism of Z@CA. A pot experiment was established to evaluate the effect of Z@CA on soil Cd(II) remediation and Cd(II) toxicity in water spinach. The results showed that in aqueous solutions, the maximum adsorption capacity of Cd(II) by Z@CA was 84.4 mg·g−1. Electrostatic attraction, ion exchange, and surface complexation collectively facilitated Cd(II) capture by Z@CA. Even after five adsorption–desorption cycles, Z@CA maintained a Cd(II) removal efficiency of 89.88 %. The results of the pot experiment showed that after applying Z@CA (2.5 w/w) in soil for 21 days, the content of bioavailable Cd(II) and total Cd(II) significantly decreased by 59.38 % and 1.75 %, respectively. The recovery rate of Z@CA reached 94.77 % and maintained its original intact structure. In addition, the Cd(II) content of water spinach was reduced by 91.43 % compared to the treatment without Z@CA, the weight, height, and relative chlorophyll content reaching 1.34, 1.73, and 1.49 times that of the treatment without Z@CA. The ideal application of Z@CA provides novel approaches and insights into the remediation of Cd(II)-contaminated soils.

From Aerial to underwater: Modeling and trajectory tracking control of the underactuated quadrotor hybrid Aerial underwater vehicle

The underactuated Quadrotor Hybrid Aerial Underwater Vehicle (HAUV) can operate in multiple mediums and seamlessly transition between them. Affected by the buoyancy, underwater control suffers a critical 180° turnover singular problem. To address this challenge, this paper presents a detailed underwater 6-degree of freedom dynamics based on the unit quaternions. A novel geometric attitude extraction method is introduced to improve the classical geometric control. Subsequently, a cascaded controller is developed for trajectory tracking. This controller consists of a position loop and an attitude loop, integrated through the attitude extraction method. It extracts the desired attitude for the inner loop from the desired thrust direction in the outer loop. Rigorous analysis demonstrates that the closed system exhibits global asymptotic stability, effectively mitigating the singular problem. Simulations demonstrate that the controller effectively adapts the quadrotor HAUV, regardless of its buoyancy (positive, negative, or neutral), to accurately track underwater trajectories and fixed points.

Asymptotic behaviors of solutions to Sobolev-type stochastic differential equations

This paper is devoted to studying the Sobolev-type stochastic differential equations with Lévy noise and mixed fractional Brownian motion. Applying a method (principle) of comparability of functions by character of Shcherbakov recurrence, it characters at least one (or exactly one) solution with the same properties as the coefficients of the equation. We establish the existence of Poisson stable solutions for the Sobolev-type equation, which includes periodic solutions, quasi-periodic solutions, almost periodic solutions, almost automorphic solutions, etc. We also obtain the global asymptotical stability of bounded Poisson stable solutions and present an example to illustrate our theoretical results.

Quantized filtering for switched memristive neural networks against deception attacks

This paper deals with the quantized mixed H∞/L2−L∞ filtering issue for switched memristive neural networks in the presence of deception attacks, in which the switching of parameters is not only subject to neural states, but also to the persistent dwell-time switching rule in the continuous-time case. First, a switched dynamic quantizer is utilized to quantize the measurement output before being transmitted to the filter. Second, deception attacks governed by a Bernoulli distribution are considered during the quantized output transmission. Then, in virtue of the Lyapunov stability theory together with stochastic analysis theory, a sufficient condition is given to ensure the global uniform asymptotic stability in the mean-square sense for the filtering error system with a mixed H∞/L2−L∞ performance. Furthermore, a co-design scheme for the desired mode-dependent filter gain and dynamic parameter is provided. Ultimately, the effectiveness of the proposed method is verified by a numerical example.

The impact of demography in a model of malaria with transmission‐blocking drugs

In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe.