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Item Open Access Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems(John Wiley & Sons, Ltd, 2020) Kashkynbayev A.; Skrzypacz P.; Kadyrov Sh.; Kaloudis K.; Bountis A.We study periodic solutions of a one-degree of freedom microelectromechanical system (MEMS) with a parallel-plate capacitor under T-periodic electrostatic forcing. We obtain analytical results concerning the existence of T-periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a T-periodic Poincaré map of the flow that these solutions are generally locally stable with large “islands” of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincaré map that stable periodic solutions with higher period nT, n>1 also exist, for wide parameter ranges, with large “islands” of bounded motion around them, within which all initial conditions avoid the pull-in instability, thus helping us significantly increase the domain of safe operation of these MEMS modelsItem Open Access Cardinality of survival set for the chaotic Tent map with holes(2020 International Young Scholars Workshop, 2020) Aitu N.; Bayadilova G.Abstract. The aim of this paper is to give an overview of the dynamics of one dimensionaldiscrete dynamical systems: Tent map family T_3, Doubling map E_2 and shift map σ are investigated. Let I-intervals(Holes) lie in the interval [0,1) and let E_2 be a Doubling map. The survivor set Ω(I) :={x∈[0,1) : E_nx /∈ I, n≥0}. Depending on location and size of the intervals we will characterize the survivor set Ω(I) infinite or finite. Also we will show conjugacy of some maps that used in this paper. By using conjugacy of functions we will show that the Survivor set is infinite or finite in another composition of maps. The Cantor sets Λ that occur as non-survivor sets for c >2 from Tent map family T_c.[1]Item Open Access MATHEMATICAL MODELING OF INFECTIOUS DISEASES AND IMPACT OF VACCINATION STRATEGIES(2022 International Young Scholars' Conference, 2022) D. Bolatova; Sh. Kadyrov; A. KaliAbstract In this work, we consider mathematical time-varying Susceptible, Exposed, Infectious, and Recovered epidemic model to study optimal vaccination strategy to control excess death due to the epidemic. We model the periodic family of vaccination strategies based on vaccination days and gaps between two periods, where we assume that a government aims to vaccinate about 80% of its population within one year. This is a constraint optimization problem, and to find the optimal vaccination strategy we used a numerical analysis approach. The mathematical models are calibrated to COVID 19 situations in Kazakhstan. Findings of the experiments suggest that to control death tolls due to disease, the governments need to offer vaccinations at the maximum possible rate without any breaks until they reach the desired 80% goal.Item Open Access The effect of quarantine measures in COVID-19(Advances in Interdisciplinary Sciences, 2020) Yergesh D.; Kadyrov Sh.; Orynbassar A.We consider deterministic SEIQR epidemic model for novel coronavirus (COVID-19). In addition to the classical SIR model, it takes into account the exposed and quarantined states. The objective of the study is to estimate epidemiological parameters for COVID-19 in the United Kingdom and understand the effect of various quarantine measures. The basic reproduction number is estimated to be 3.622. The findings suggest that weaker quarantine measures may be insufficient to fight with the disease.Item Open Access Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems(Mathematical Methods in the Applied Sciences, 2020) Kadyrov Sh.; Kashkynbayev A.; Skrzypacz P.; Kaloudis K.; Bountis A.We study periodic solutions of a one-degree of freedom microelectromechanical system (MEMS) with a parallel-plate capacitor under T-periodic electrostatic forcing. We obtain analytical results concerning the existence of T-periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a T-periodic Poincaré map of the flow that these solutions are generally locally stable with large “islands” of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincaré map that stable periodic solutions with higher period nT, n>1 also exist, for wide parameter ranges, with large “islands” of bounded motion around them, within which all initial conditions avoid the pull-in instability, thus helping us significantly increase the domain of safe operation of these MEMS models.