Global Stability Research Articles

Influence of immersed particles on the stability of the liquid–liquid interface in a two-layer channel flow

The current study investigates the global linear stability of a two-layer channel flow with a train of solid particles flowing near the liquid–liquid interface. Three different mechanisms of instability (shear, interfacial and migration modes) are identified, and their interactions are examined. The interfacial instability, associated with the viscosity jump at the liquid–liquid interface, is found to be coupled to the migration of the particle. The stability of the flow configuration is evaluated for various governing parameters, including fluid viscosities and flow rate ratios, particle position, inter-particle distance, and Reynolds and capillary numbers. Our numerical results are compared with the particle-free flow configuration, indicating that the presence of the particle in the more viscous fluid promotes the destabilization of the interface. Remarkably, under certain flow parameters, the presence of the particle stabilizes the interface when flowing in the less viscous liquid. The impact of particles is more significant as the capillary number increases or the Reynolds number decreases.

Dynamics of Oscillator Populations Globally Coupled with Distributed Phase Shifts.

We consider a population of globally coupled oscillators in which phase shifts in the coupling are random. We show that in the maximally disordered case, where the pairwise shifts are independent identically distributed random variables, the dynamics of a large population reduces to one without randomness in the shifts but with an effective coupling function, which is a convolution of the original coupling function with the distribution of the phase shifts. This result is valid for noisy oscillators and/or in the presence of a distribution of natural frequencies. We argue also, using the property of global asymptotic stability, that this reduction is valid in a partially disordered case, where random phase shifts are attributed to the forced units only. However, the reduction to an effective coupling in the partially disordered noise-free situation may fail if the coupling function is complex enough to ensure the multistability of locked states.

A Complex Dynamic of an Eco-Epidemiological Mathematical Model with Migration

In this paper, we propose an eco-epidemiological mathematical model in order to describe the effect of migration on the dynamics of a prey–predator population. The functional response of the predator is governed by the Holling type II function. First, from the perspective of mathematical results, we develop results concerning the existence, uniqueness, positivity, boundedness, and dissipativity of solutions. Besides, many thresholds have been computed and used to investigate the local and global stability results by using the Routh–Hurwitz criterion and Lyapunov principle, respectively. We have also established the appearance of limit cycles resulting from the Hopf bifurcation. Numerical simulations are performed to explore the effect of migration on the dynamic of prey and predator populations.

Interplay of International Law and Cyberspace: State Sovereignty Violation, Extraterritorial Effects, and the Paradigm of Cyber Sovereignty

Abstract Information and communication technology (ICT) threats, involving malicious use of ICTs, pose substantial risks to global security and stability. These threats, emanating from State and non-State actors, endanger economic growth, societal well-being, and human safety. The existing international legal framework struggles to adequately confront these challenges, resulting in issues concerning State sovereignty, cyber-attacks on critical infrastructure, and the emergence of cyberspace sovereignty. Cyber-attacks targeting key infrastructure can undermine sovereignty by aiding another State’s territorial control. The enforcement of cyberspace legislation, whether regional or intra-State, can infringe upon other States’ sovereignty due to cross-border repercussions. Despite the presence of numerous international and regional regulations, enforcement remains lacking. The concept of cyberspace sovereignty has arisen with technological advancements, signifying a need for digital realm sovereignty. Yet, this form of sovereignty is narrower compared to territorial sovereignty. This article delves into the nexus between international law, State sovereignty, and ICT threats, along with the progression of cyberspace sovereignty. Through qualitative analysis of primary and secondary sources, it examines the application of existing international law in the digital landscape. By scrutinizing these intricacies, the paper endeavors to comprehend the contemporary challenges posed to international law and explore potential resolutions.

A tuberculosis model with three infected classes

The dynamics of tuberculosis within a population cannot be adequately represented by a single infectious class. Therefore, this study develops a compartmental model encompassing latent, active, and drug-resistant populations to better capture tuberculosis dynamics in a community. Model analysis reveals that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number is below one. Moreover, the use of a suitable Lyapunov function demonstrates global asymptotic stability of the disease-free equilibrium point. An endemic equilibrium emerges when the basic reproduction number exceeds one. Sensitivity analysis is conducted for each parameter associated with the basic reproduction number, and optimal control analysis is employed to assess the impact of various control strategies on disease containment. Numerical simulations are conducted to supplement theoretical findings, illustrating the practical implications of the proposed control strategies.

How Drivers Lose Control of the Car

<div>After a severe lane change, a wind gust, or another disturbance, the driver might be unable to recover the intended motion. Even though this fact is known by any driver, the scientific investigation and testing on this phenomenon is just at its very beginning, as a literature review, focusing on SAE Mobilus<sup>®</sup> database, reveals. We have used different mathematical models of car and driver for the basic description of car motion after a disturbance. Theoretical topics such as nonlinear dynamics, bifurcations, and global stability analysis had to be tackled. Since accurate mathematical models of drivers are still unavailable, a couple of driving simulators have been used to assess human driving action. Classic unstable motions such as Hopf bifurcations were found. Such bifurcations seem almost disregarded by automotive engineers, but they are very well-known by mathematicians. Other classic unstable motions that have been found are “unstable limit cycles.” The driving simulator results have been reproduced by experimental tests on track. We have assessed that the driver’s steering action can make the car motion unstable if a proper disturbance has acted. The delay of the driver’s steering action is the primary cause for the generation of limit cycles. Future automated vehicles should be conceived by focusing on the addressed phenomenon.</div>

Global stability design of concrete-filled corrugated steel tubular columns

In recent years, various types of concrete-filled steel tubular (CFST) columns were proposed and they have been widely used in engineering practice. Considering the great confinement effect of corrugated steel plate on the concrete, a novel type of CFST column called concrete-filled corrugated steel tubular (CFCST) column was proposed. The CFCST column consists of horizontally corrugated steel plates, corner steel bars and infilled concrete. In this paper, the stability performance of CFCST columns is studied. Firstly, a finite element (FE) model was developed for numerical simulation. The ultimate resistances, load-displacement curves and failure modes obtained from the FE models were compared with previous test results to verify the validity of the FE model. Subsequently, seven sets of numerical examples were analyzed to investigate the impact of key parameters on the global stability performance of CFCST columns. These examples involved variations in geometric dimensions, corrugation shapes and material strengths. Finally, the stability coefficients φ of CFCST columns obtained from FE numerical simulation were compared to several existing stability curves. On this basis, a new stability curve was proposed for predicting the global stability resistance of CFCST columns with good accuracy and reasonable redundancy.

Global dynamics of heterogeneous epidemic models with exponential and nonexponential latent period distributions

AbstractMany epidemic models assume an exponential distribution for the latent stage, but this may not accurately represent reality and could impact disease transmission predictions. Previous studies for short time scale models have shown that the choice of latency distribution affects estimates of the epidemic peak, time to peak, and infection eradication time, but has little effect on the final infection size. However, it is unclear if these conclusions hold for long time scale models. To address this, we investigate the impact of different latency distributions on disease dynamics in long‐term models, comparing them with short‐term models. We propose two susceptible‐exposed‐infected‐hospitalized‐recovered () models with multiple groups, using exponential and gamma distributions for latency. We derive the basic reproduction number () for both models and prove the global stability of the equilibrium points. We conduct numerical simulations and find that the gamma distribution may lead to larger epidemic peak sizes and longer peak times compared to the exponential distribution. However, the impact of latency distribution on estimating the peak and time to peak is smaller in long‐term models than in short‐term models. Additionally, the effect on the final total infected size is negligible regardless of the time scale. Therefore, when analyzing long‐term epidemic dynamics using heterogeneity models, the choice of latency distribution does not significantly affect the results. Assuming an exponential distribution for the latency is sufficient for simplifying the model and facilitating analysis. Our study provides valuable insights for selecting appropriate mathematical models in epidemiology.

A caputo fractional-order model of tuberculosis incorporating enlightenment and therapy using the Laplace-Adomian decomposition method

ABSTRACT In this study, we used a deterministic model to investigate tuberculosis transmission dynamics while considering control measures. We analyzed four compartmental models representing susceptible, latent, infected, and recovered populations. To assess the potential spread of the disease, we calculated the basic reproduction number using the next-generation matrix after establishing a disease-free equilibrium. Additionally, we explored the endemic equilibrium, as well as local and global stabilities. To obtain numerical solutions, we employed the Laplace-Adomian decomposition method. For constructing the model, we utilized Maple 18 software and varied the order (0 < ψ < 1) to examine the impact of enlightenment and therapy. Graphical representations were used to analyze the effects of non-integer order Caputo derivative parameters on the susceptible, latent, infected, and recovered populations over time. Our detailed discussion highlights the crucial role of mathematical models based on Caputo fractional derivatives in effectively controlling and eradicating tuberculosis from society. These findings contribute valuable insights to inform strategies for combating the disease and promoting public health initiatives.

Stability of impulsive stochastic functional differential equations with delays

In this paper, we consider the global asymptotical stability of stochastic functional differential equations with impulsive effects. First, by constructing the Lyapunov function, some stability criteria of impulsive stochastic functional differential equations are established. Second, we propose an application to investigate the effectiveness of the obtained results.

Cybercrimes: An Emerging Category of Offenses within the Frame of the International Criminal Court Jurisdiction

In our interconnected society, crime persists, demanding joint efforts by national and international authorities to detect, prevent, and prosecute criminal activities. Jurisprudential evolution mandates lawmakers to possess a comprehensive legal vision, adapting laws to changing social contexts and emerging criminal methods, especially in technology, including computer technology and Artificial Intelligence (AI). This article comments on the escalating vulnerability of sovereign states and their economies to cyber-attacks. The radical evolution of computer systems has led to new modes of aggression, targeting not only traditional legal assets but also individuals familiar with advanced technology. The emergence of "cyberwarfare" prompts inquiries into potential categorizations within international legal frameworks. Recent global conflicts highlight the potential classification of cyber-attacks on critical infrastructure as war crimes or acts of aggression, urging the International Criminal Court (ICC) to consider incorporating cybercrimes into its core interests. While normative references may lack in existing conventions, the Martens Clause emphasizes treating attacks using technology as equivalent to conventional means. Article 51 of the United Nations Charter implies that cyber weapons could be deemed equivalent to conventional weapons under international law. The article stresses the importance of education and advanced training for legal personnel skilled in identifying cybercrime perpetrators, challenging the ICC to recruit or train individuals with the necessary legal and technical expertise for effective cybersecurity responses. The article briefly explores challenges in conceptualizing and categorizing cybercrimes within existing legal frameworks. The intersection of law and technology necessitates harmonious collaboration between legal and technical experts, acknowledging the intricate web of cyberspace and the implications of cyber threats on global stability and security. In conclusion, the article advocates a fundamental shift in the approach to justice, recognizing the ICC's imperative evolution in addressing cybercrimes. Integrating cybercrimes into the ICC's purview aligns with international law principles, emphasizing the equivalence of cyber weapons to conventional arms. Collaboration between legal and technical experts is essential in navigating the complexities of cybercrimes, ensuring accountability, and upholding justice in the digital age. The article concludes by highlighting the proactive role of the ICC in shaping the future of global justice amid emerging cyber threats.

The effect of migration on the transmission of HIV/AIDS using a fractional model: Local and global dynamics and numerical simulations

Human immunodeficiency virus (HIV) is a serious disease that threatens and affects capital stock, population composition, and economic growth. This research paper aims to study the mathematical modeling and disease dynamics of HIV/acquired immunodeficiency syndrome (AIDS) with memory effect. We propose two fractional models in the Caputo sense for HIV/AIDS with and without migration. First, we prove the existence and positivity of both models and calculate the basic reproduction number using the next generation method. Then, we study the local and global stability of the obtained equilibria. In addition, numerical simulations are provided for different values of the fractional order using the Adams–Bashforth–Moulton fractional scheme, to verify the theoretical results. Moreover, a sensitivity analysis of the parameters for the model with migration is carried out.

Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey

The stability analysis of an epidemic model that takes into account the impact of vaccination and hospitalization is investigated in this study. Disease-free and endemic equilibrium points are obtained for the stability analysis. The necessary conditions for analyzing local stability at equilibrium points as well as global stability at the disease-free equilibrium point are also defined. Using data from three different periods corresponding to the emergence of three different variants of the COVID-19 outbreak in Turkey, the numerical simulation with graph fitting for the model is also taken into account. The analysis considers the efficacy of vaccination in restricting the virus's spread.

Analysis of a patch epidemic model incorporating population migration and entry–exit screening

This paper presents an SIQR patch model that combines population migration and entry–exit screening. The threshold for disease extinction is determined using the next-generation matrix method. By constructing the Lyapunov function, the global asymptotic stability of the disease-free equilibrium is demonstrated when R0 &amp;lt; 1. The local asymptotic stability of the endemic equilibrium is shown using the Hurwitz criterion, and it is found that the disease is uniformly persistent when R0 &amp;gt; 1. The influence of screening and migration on disease dynamics is discussed via numerical simulations. Our findings highlight the significance of the detection rate as a vital index in disease transmission and emphasize the effectiveness of screening strategies in preventing outbreaks. Therefore, during an outbreak, it is recommended to establish checkpoints in regions with high mobility to identify and isolate potentially infected individuals, thereby reducing the widespread dissemination of the pandemic.

SIS Epidemic Spreading Under Multilayer Population Dispersal in Patchy Environments

We study SIS epidemic spreading models under population dispersal on multi-layer networks. We consider a patchy environment in which each patch comprises individuals belonging to different classes. Individuals disperse to other patches on a multi-layer network in which each layer corresponds to a class. The dispersal on each layer is modeled by a Continuous Time Markov Chain (CTMC). At each time, individuals disperse according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS model. We establish the existence of various equilibria under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We also derive simple conditions that highlight the influence of the multi-layer network on the stability of these equilibria. For this model, we study optimal intervention strategies using a convex optimization framework. Finally, we numerically illustrate the influence of the multi-layer network structure and the effectiveness of the optimal intervention strategies.

Global dynamics and optimal control of a nonlinear fractional-order cholera model

In this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asymptotic stability of the equilibrium points have been established using appropriate Lyapunov functional. Moreover, a fractional-order control problem is presented, and its analytical solution is derived using Pontryagin’s maximum principle. Also, some graphical visualizations of the theoretical results are provided. It is found that the factional-order derivative only affect the time to reach the stationary states. Sensitivity analysis reveals that by reducing the rates of new recruitment and both the disease transmission rates, it may be possible to reduce the value of the basic reproduction number.

Global asymptotic stability of endemic equilibria and stability of traveling waves for a diffusive SIR epidemic model with logistic growth

AbstractThis paper deals with the asymptotic behavior of solutions for the diffusive epidemic model with logistic growth. In the first part, we consider the initial boundary value problem on the bounded domain and derive the stabilization of the solutions of the reaction–diffusion system to a constant equilibrium. In the second part, we consider the initial value problem on $${\mathbb {R}},$$ R , and derive the stability of forced waves under certain perturbations of a class of initial data.

Modelling the Use of the Trace-Test-Isolate-Treat Strategy for Controlling the Spread of COVID-19

During the COVID-19 pandemic that ravaged the entire world between 2019 and 2021, the Trace-Test-Isolate-Treat Strategy was devised as an emergency way of managing the spread of the disease. As the name implies, the Trace-Test-Isolate-Treat Strategy involves identifying those who had contact with an infected person through contact tracing, and subsequent isolation and treatment if confirmed to be infected with the disease. This paper aims to model the transmission dynamics of COVID-19, with the Trace-Test-Isolate-Treat Strategy as a control strategy. To do this, we propose a simple nonlinear system of ordinary differential equations that models COVID-19 dynamics and incorporates the Trace-Test-Isolate-Treat strategy as a way of controlling the spread of the disease. The analysis of the model shows that the disease-free equilibrium is locally asymptotically stable if the reproduction number, R_eff is less than one. Furthermore, the model is shown to possess a unique and stable endemic equilibrium if, R_eff&gt;1. This confirms the global asymptotic stability of the disease-free equilibrium and the absence of backward bifurcation in the model. Numerical plots show the effectiveness of isolation and treatment of infected persons in reducing the spread of the disease.

Predictor-Based Decentralized Event-Triggered Secure Control for Nonlinear Cyber-Physical Systems Under Replay Attacks and Time Delay

This paper investigates the problem of predictor-based decentralized event-triggered secure control for nonlinear cyber-physical systems (CPSs) subject to replay attacks and time delay. To overcome the limitation of the network bandwidth, a periodic decentralized event-triggered scheme (PDETS) is designed for non-strict feedback nonlinear CPSs in the presence of replay attacks. Then, decentralized output feedback controllers are constructed by designing predictor-based observers to attenuate the influences of replay attacks and time delay. Based on the proposed new framework, the global exponential stability (GES) of the resulting nonlinear CPSs can be guaranteed. Finally, two application examples verify the effectiveness of the proposed method.

Dynamic behavior of enzyme kinetics cooperative chemical reactions

This article uses computational mathematics to investigate the dynamics of cooperative occurrences in chemical reactions inside living organisms. We study the dynamics of complex systems using mathematical models based on ordinary differential equations, paying special attention to chemical equilibrium and reaction speed. Explanations of cooperation, non-cooperation, and positive cooperation are presented in our study. We analyze the stabilities of equilibrium points by a systematic analysis that makes use of the Jacobian matrix and the threshold parameter R0. We next extend our investigation to evaluate global stability and the probability of the model. Variations in k3 have a notable effect on substrate concentration probabilities, indicating that it plays an important role in reaction kinetics. Reducing k3 highlights the substrate's critical contribution to the system by extending its presence in the concentration. We find that different results were obtained for cooperative behavior: higher reaction rates at different binding sites are correlated with positive cooperativity, while slower reactions are induced by negative cooperativity. The Adams–Bashforth method is used to show numerical and graphical solutions with the help of MATLAB. Tables and graphs are used to further explain the effects of the parameters. This study underlines how well ordinary differential equations may represent the complicated system dynamics found in chemical reactions. It also provides elusive insights into cooperative occurrences, which develops our understanding of the phenomenon and serves as a foundation for future research.