аналіз стійкості

Spatiotemporal dynamics of RNA viruses in the presence of immunity and treatment: case of SARS-CoV-2

In this paper, we develop a mathematical model using partial differential equations to investigate the behavior of RNA viruses in the presence of antiviral treatment.  The developed model includes both cell-to-cell and virus-to-cell modes of transmission.  Initially, we establish the well-posedness of the model by demonstrating the existence and uniqueness of solutions, as well as their positivity and boundedness.  Additionally, we identify and analyze the stable equilibrium states, their global stability depending on specific threshold parameters, using Lyapunov functi

Numerically investigating the effects of slip and thermal convective on nanofluid boundary layer past a stretching/shrinking surface

The study is focusing on the steady boundary layer flow, heat and mass transfer passing through stretching/shrinking sheet immersed in nanofluid in the presence of the second order slip velocity and thermal convective at the boundary.  The governing partial differential equations are converted into ordinary differential equations by applying the similarity variables before being solved computationally using bvp4c function in Matlab software.  The results of skin friction, heat transfer as well as mass transfer coefficient on the governing parameter such as the first ord

An epidemic model with viral mutations and vaccine interventions

In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration.  We discuss and analyze the existence and stability of equilibrium points.  This model has three types of equilibrium points, namely disease-free equilibrium, dominance equilibrium point of strain two, and coexistence endemic equilibrium point.  The local stability of the dominance equilibrium point of strain two and coexistence endemic equilibrium point are verified by using the Routh--Hurwitz criteria, while for the global stability of the dominance equilibrium point of strain two,

Study of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs

In this paper, we have a discrete delayed dynamic system of three marine species: prey, predator, and superpredator.  In addition to the effect of prey toxicity, we consider the negative fishing effect of these species.  The study of this model consists of the search for equilibria with eigenvalue analysis, the existence of Hopf bifurcations at interior equilibria, and the determination of direction and stability analysis of Hopf bifurcation using the theory of normal form and center manifold.  Some examples are given with numerical simulations to illustrate the results

Double solutions and stability analysis of slip flow past a stretching/shrinking sheet in a carbon nanotube

A stagnation point flow past a stretching/shrinking surface in carbon nanotubes (CNTs) with slip effects is investigated in this paper.  Applying transformations of similarity, the governing partial differential equations are modified to the nonlinear ordinary differential equations.  Afterward, they are numerically solved in Matlab by the bvp4c solver.  The single-wall CNTs and multi-wall CNTs are used, including water as a base fluid.  The effects of the flow parameters are investigated, shown in the form of graphs, and physically evaluated for the dimensionless velocity, temperature, ski

Radiative flow of magnetic nanofluids over a moving surface with convective boundary condition

The influence of convective boundary conditions and heat radiation on magnetic nanofluids (MNFs) flowing through a permeable moving plate is investigated numerically in this study.  The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable similarity variables.  The ODEs are solved by implementing the built-in solver in Matlab called bvp4c.  The stability analysis has supported our initial presumption that only the first solution is stable.  The thermal performance between cobalt ferrite nanofluid and manganese-zinc ferrit

A fractional-order model for drinking alcohol behaviour leading to road accidents and violence

In this paper, we propose a new fractional-order model of alcohol drinking involving the Caputo derivative and six groups of individuals.  We introduce road accidents and violence related to alcohol consumption as separate classes to highlight the role of alcoholism in the aggressive and risky behaviour of heavy drinkers.  We show the existence and uniqueness of the non-negative solutions, and we determine the basic reproduction number $R_{0}$.  The sensitivity analysis of the model parameters is performed to characterize the important parameters that have the most effe

Робастна стійкість дробових електромеханічних систем

Розроблено інженерну методику визначення робастної стійкості для електро- механічних систем (ЕМС), які описано моделями дробового порядку. Проаналізовано динамічні ЕМС, які описано передавальними функціями з дробовим характеристичним поліномом з трьома членами. Проаналізовано стійкість таких систем з використанням комплексної площини Рімана. Встановлено взаємозв’язок між секторами, в яких можуть перебувати полюси дробової ЕМС, та станом таких систем з погляду стійкості та можливості їх фізичної реалізації.